9408.json

{
    "9408/hep-ph9408397_arXiv.txt": {
        "abstract": "Using the latest results from the solar neutrino experiments and a few standard assumptions, I show that the popular solar models are ruled out at the 3$\\sigma$ level or at least {\\em two} of the experiments are incorrect. Alternatively, one of the assumptions could be in error. These assumptions are spelled out in detail as well as how each one affects the argument. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9408/astro-ph9408002_arXiv.txt": {
        "abstract": "s#1{{ \\centering{\\begin{minipage}{30pc}\\tenrm\\baselineskip=12pt\\noindent \\centerline{\\tenrm ABSTRACT}\\vspace{0.3cm} \\parindent=0pt #1 \\end{minipage} }\\par}}  \\newcommand{\\bibit}{\\it} \\newcommand{\\bibbf}{\\bf} \\renewenvironment{thebibliography}[1] {\\begin{list}{\\arabic{enumi}.} {\\usecounter{enumi}\\setlength{\\parsep}{0pt} \\setlength{\\leftmargin 1.25cm}{\\rightmargin 0pt} \\setlength{\\itemsep}{0pt} \\settowidth {\\labelwidth}{#1.}\\sloppy}}{\\end{list}}  \\topsep=0in\\parsep=0in\\itemsep=0in \\parindent=1.5pc  \\newcounter{itemlistc} \\newcounter{romanlistc} \\newcounter{alphlistc} \\newcounter{arabiclistc} \\newenvironment{itemlist} {\\setcounter{itemlistc}{0} \\begin{list}{$\\bullet$} {\\usecounter{itemlistc} \\setlength{\\parsep}{0pt} \\setlength{\\itemsep}{0pt}}}{\\end{list}}  \\newenvironment{romanlist} {\\setcounter{romanlistc}{0} \\begin{list}{$($\\roman{romanlistc}$)$} {\\usecounter{romanlistc} \\setlength{\\parsep}{0pt} \\setlength{\\itemsep}{0pt}}}{\\end{list}}  \\newenvironment{alphlist} {\\setcounter{alphlistc}{0} \\begin{list}{$($\\alph{alphlistc}$)$} {\\usecounter{alphlistc} \\setlength{\\parsep}{0pt} \\setlength{\\itemsep}{0pt}}}{\\end{list}}  \\newenvironment{arabiclist} {\\setcounter{arabiclistc}{0} \\begin{list}{\\arabic{arabiclistc}} {\\usecounter{arabiclistc} \\setlength{\\parsep}{0pt} \\setlength{\\itemsep}{0pt}}}{\\end{list}}  \\newcommand{\\fcaption}[1]{ \\refstepcounter{figure} \\setbox\\@tempboxa = \\hbox{\\tenrm Fig.~\\thefigure. #1} \\ifdim \\wd\\@tempboxa > 6in {\\begin{center} \\parbox{6in}{\\tenrm\\baselineskip=12pt Fig.~\\thefigure. #1 } \\end{center}} \\else {\\begin{center} {\\tenrm Fig.~\\thefigure. #1} \\end{center}} \\fi}  \\newcommand{\\tcaption}[1]{ \\refstepcounter{table} \\setbox\\@tempboxa = \\hbox{\\tenrm Table~\\thetable. #1} \\ifdim \\wd\\@tempboxa > 6in {\\begin{center} \\parbox{6in}{\\tenrm\\baselineskip=12pt Table~\\thetable. #1 } \\end{center}} \\else {\\begin{center} {\\tenrm Table~\\thetable. #1} \\end{center}} \\fi}  \\def\\@citex[#1]#2{\\if@filesw\\immediate\\write\\@auxout {\\string\\citation{#2}}\\fi \\def\\@citea{}\\@cite{\\@for\\@citeb:=#2\\do {\\@citea\\def\\@citea{,}\\@ifundefined {b@\\@citeb}{{\\bf ?}\\@warning {Citation `\\@citeb' on page \\thepage \\space undefined}} {\\csname b@\\@citeb\\endcsname}}}{#1}}  \\newif\\if@cghi \\def\\cite{\\@cghitrue\\@ifnextchar [{\\@tempswatrue \\@citex}{\\@tempswafalse\\@citex[]}} \\def\\citelow{\\@cghifalse\\@ifnextchar [{\\@tempswatrue \\@citex}{\\@tempswafalse\\@citex[]}} \\def\\@cite#1#2{{$\\null^{#1}$\\if@tempswa\\typeout {IJCGA warning: optional citation argument ignored: `#2'} \\fi}} \\newcommand{\\citeup}{\\cite}  \\def\\fnm#1{$^{\\mbox{\\scriptsize #1}}$} \\def\\fnt#1#2{\\footnotetext{\\kern-.3em {$^{\\mbox{\\sevenrm #1}}$}{#2}}}  \\font\\twelvebf=cmbx10 scaled\\magstep 1 \\font\\twelverm=cmr10 scaled\\magstep 1 \\font\\twelveit=cmti10 scaled\\magstep 1 \\font\\elevenbfit=cmbxti10 scaled\\magstephalf \\font\\elevenbf=cmbx10 scaled\\magstephalf \\font\\elevenrm=cmr10 scaled\\magstephalf \\font\\elevenit=cmti10 scaled\\magstephalf \\font\\bfit=cmbxti10 \\font\\tenbf=cmbx10 \\font\\tenrm=cmr10 \\font\\tenit=cmti10 \\font\\ninebf=cmbx9 \\font\\ninerm=cmr9 \\font\\nineit=cmti9 \\font\\eightbf=cmbx8 \\font\\eightrm=cmr8 \\font\\eightit=cmti8  \\noindent \\makebox[0pt][l]{ \\raisebox{36pt}[0pt][0pt]{astro-ph/9408002, UCLA-ASTRO-ELW-94-01}}  \\centerline{\\tenbf DARK MATTER IN THE LIGHT OF COBE\\,\\footnotemark[1] \\footnotetext[1]{The National Aeronautics and Space Administration/Goddard Space Flight Center (NASA/GSFC) is responsible for the design, development, and operation of the Cosmic Background Explorer (\\COBE). Scientific guidance is provided by the \\COBE\\ Science Working Group. GSFC is also responsible for the development of the analysis software and for the production of the mission data sets.} }  \\pagestyle{empty}  \\vspace{0.8cm}  \\centerline{\\tenrm EDWARD L. WRIGHT} \\baselineskip=13pt \\centerline{\\tenit UCLA Astronomy} \\baselineskip=12pt \\centerline{\\tenit Los Angeles CA 90024-1562}  \\abstracts{The observations of all three \\COBE\\ instruments are examined for the effects of dark matter. The anisotropy measured by the DMR, and especially the degree-scale ground- and balloon-based experiments, is only compatible with large-scale structure formation by gravity if the Universe is dominated by non-baryonic dark matter. The FIRAS instrument measures the total power radiated by cold dust, and thus places tight limits on the absorption of starlight by very cold gas and dust in the outer Milky Way. The DIRBE instrument measures the infrared background, and will place tight limits on the emission by low mass stars in the Galactic halo. }  \\parindent 20pt \\baselineskip 14pt ",
        "introduction": "While \\COBE\\ (Boggess \\etal\\ 1992) has no instruments that directly detect dark matter, its three instruments offer important clues about the baryonic and non-baryonic content of the Universe.  The FIRAS observations of the spectrum of the cosmic microwave background radiation (CMBR) show that any deviation from a blackbody are very small (Mather \\etal\\ 1990 and Mather \\etal\\ 1994).  This limits the possible effect of energetic explosions on the formation of large-scale structure (Wright \\etal\\ 1994).  If gravity is the force responsible for large-scale structure, then the DMR observations of anisotropy require a non-baryonic dark matter dominated Universe.  Even the baryons in the Universe are mostly in a dark form, but FIRAS observations of the millimeter emission from the Galaxy show that these dark baryons can not be in clouds of very cold gas and dust associated with the CO absorbing clouds seen by Lequeux \\etal\\ (1993).  However, even more compact configurations of baryons are allowed: brown dwarfs.  A Galactic halo of old cold brown dwarfs will be essentially undetectable by the DIRBE instrument unless all of the mass is in objects right at the limit of hydrogen burning.  \\newpage  \\section {DMR $\\Delta T$ and non-Baryonic Dark Matter}  \\begin{figure}[t] \\plotone{baryon.ps} \\caption{Predicted $\\Delta T$ for Holtzman models at 0.5$^\\circ$ scale \\vs\\ quadrupole scale.} \\label{baryon} \\end{figure}  The DMR anisotropy implies a small level of gravitational potential perturbations via the Sachs-Wolfe (1967) effect.  At the same time, models of large-scale structure formation require certain levels of gravitational forces which can be converted into predicted $\\Delta T$'s.  Figure \\ref{baryon} shows the predictions from the models of Holtzman (1989) compared to the \\COBE\\ DMR \\Amp\\ and the anisotropy at 0.5$^\\circ$ measured by the MAX experiment (Clapp \\etal\\ 1994 and Devlin \\etal\\ 1994).  The models with only baryonic matter are surrounded by open diamonds, while models emphasized by Wright \\etal\\ (1992) are surrounded by open circles.  The CDM+baryon model and the vacuum dominated model (which still has 90\\% of the matter non-baryonic) both sit on top of the observed $\\Delta T$'s, while the open model and the mixed dark matter model need bias factors $b_8 < 2$ to agree with the data. The nearest baryonic model needs $b_8 \\approx 10$ to fit the data, which is not reasonable.  This problem with baryonic models arises because non-baryonic dark matter perturbations start to grow at $z_{eq} \\approx 6000$, while baryonic perturbations can only start to grow at $z_{rec} \\approx 10^3$, and thus lose a factor of $\\gsim 6$ in growth. ",
        "conclusions": "The observations by \\COBE\\ of the CMBR show no evidence for non-gravitational forces producing large-scale structure.  The gravitational forces implies by the DMR measurements of $\\Delta T$ are sufficient to produce the observed large-scale structure only if most of the matter in the Universe responds freely to these gravitational forces before recombination, which requires non-baryonic dark matter.  The baryonic dark matter cannot be very cold gas and dust associated with the CO absorption lines seen by Lequeux because it would produce too much millimeter wave emission from the Galactic plane. However, the dark baryons can easily be brown dwarfs which will escape detection by \\COBE\\ and ground-based IR surveys but may well be seen by \\SIRTF."
    },
    "9408/astro-ph9408066_arXiv.txt": {
        "abstract": " ",
        "introduction": "By `large scale structure' one means galaxies and clusters, with emphasis on their spatial distribution and motions, and also the cosmic microwave background (cmb) anisotropy. We are at present on the verge of a quantum leap in our understanding of large scale structure, because the cmb anisotropy is being measured for the first time \\cite{smet,gorski,scottrev,scottwhite}. In particular, we may in the forseeable future verify or rule out the standard model of structure formation, according to which large scale structure arises from a Gaussian, adiabatic density perturbation that is nearly scale invariant at horizon entry. If that model is verified there will be  the dazzling prospect of a window on the fundamental interactions on scales approaching the Planck scale, because the vacuum fluctuation during inflation generates just such a perturbation.  This article has two objectives. One is to equip the non-specialist with a starting point, from which to follow the saga that will unfold during the coming years. To this end we include an extensive discussion of linear perturbation theory, which allows one to translate theoretical input coming from say a model of inflation into a form amenable for comparison with observations. Our other aim is to provide a critical assessment of the present position, in the light of all relevant observations, including the abundance of damped Lyman alpha systems and the latest analysis of the crucial COBE data. These and the other relevant observations are summarized on a single plot. On the same plot are drawn the canonical version of the standard model, and variants which alter the Hubble constant $h$, the spectral index $n$, and the fraction $\\Omega_\\nu$ of any hot dark matter. We discuss the observational constraints on these three parameters, and in particular the constraint on $n$, which is of great interest because it can be a sensitive discriminator between inflationary models. As we have emphasised several times in earlier publications \\cite{will,LL1,LL2,mymnras,berkeley,capri} a powerful constraint on $n$ is provided by the long `lever arm' between the very large scale explored by the large angle cmb anisotropy and the smaller scales explored by galaxy and cluster data. On the basis of the presently available data we find that $0.6<n<1.1$, with lower limit tightened to $0.8$ in particle physics motivated models of inflation that generate significant gravitational waves. The lower limit in particular is rather firm because several different types of observation confirm it.  \\subsection*{Three possible models for large scale structure}  Three possible models of large scale structure are commonly entertained. The standard model is that it originates as a Gaussian adiabatic density perturbation, whose spectrum is nearly scale independent at horizon entry. This model has been explored far more thoroughly than the other two, and is the only one that will be considered here. An alternative is that large scale structure originates from topological defects, such as cosmic strings. In both of these models the underlying scale invariance means that galaxy and cluster formation is directly related to the magnitude of the large scale cmb anisotropy. It also means that the first objects to form are the progenitors of galaxies. Finally there is the possibility that large scale structure originates from a density perturbation (either adiabatic or isocurvature) with a spectrum that is not even approximately scale independent. In that case structure formation could be very different, with perhaps much lighter objects forming first, and it would not be directly related to the magnitude of the large scale cmb anisotropy.  The standard model has two features which distinguish it from the others, and make it so attractive. One of them concerns theory. If, as is widely supposed, the initial conditions for the hot big bang are set by inflation, then an adiabatic, Gaussian, more or less scale invariant density perturbation is {\\em predicted}. What could be more natural than to suppose that perturbation will explain large scale structure? If that turns out to be so, large scale structure will provide us with a unique window on the nature of the fundamental interactions, because both the magnitude and precise scale dependence of the perturbation are highly model dependent \\cite{LL1,paul,davesal,mymnras}.  The other feature concerns phenomenology. The model has been intensively studied and is relatively simple, so that by now one knows how to estimate its predictions for most available types of data. To a first approximation the predictions depend on a single number, specifying the magnitude of the density perturbation at horizon entry. If that number is chosen to fit the cmb anisotropy, all other data can certainly be explained to within a factor of two or three! Of course the burning question is whether the data can actually be explained within their observational uncertainties, which in the best cases are only tens of percent. The answer to that question depends what other parameters are available in the standard model, and it will be our main focus.  \\subsection*{An overview of the standard model}  The standard model assumes that large scale structure originates as an adiabatic, Gaussian density perturbation whose spectrum is more or less scale-independent at horizon entry. The scale dependence (if any) is parameterised as a power law, with a spectral index that by convention is defined so that $n=1$ corresponds to scale invariance.  In order to have any chance of agreeing with observation, the standard model requires non-baryonic dark matter, which is more or less cold, and which has a density dominating the baryon density. By `cold' one means that the constituent particles are stable, non-interacting and non-relativistic, at all relevant epochs.  The simplest version of the standard model assumes that $n=1$, and that the (non-baryonic) dark matter is completely cold. It also assumes that the energy density of the universe is critical, $\\Omega=1$, with no cosmological constant or other exotic contribution so that there is the standard cosmology with matter domination at present. This critical density, $n=1$ CDM model was the favoured one for many years. It contains only two free parameters, which are the normalisation of the spectrum, and the value of the Hubble constant $H_0\\equiv100h\\km\\sunit\\mone \\Mpc\\mone$. According to observations having nothing to do with large scale structure (namely, direct observations and measurements of the age of the universe), $0.4\\lsim h\\lsim 0.6$.\\footnote{Higher values of $h$ are permitted only in low density models, especially those featuring a cosmological constant. Given $h$, the baryon density is practically fixed by the standard nucleosynthesis relation $\\Omega_B h^2=0.013\\pm 0.002$.} Assuming the central value $h=0.5$ we arrive at a canonical version of the CDM model, whose only free parameter is the magnitude of the scale invariant density perturbation.  The canonical CDM model does not agree with observation because the predicted spectrum of the density perturbation has the wrong scale dependence. On large scales the spectrum is accurately determined by the COBE measurement of the cmb anisotropy, and as one goes down in scale through the regime explored by data on galaxies and clusters it becomes progressively too big compared with the data. How can we reduce the small scale power?  The simplest possibility is to reduce $h$ below the canonical value $h=0.5$, which reduces the small scale density perturbation because it delays matter domination giving the density perturbation less time to grow. It has recently been noted \\cite{lowh} that this `old universe' option might work if $h$ is as low as $0.3$, but such a value is difficult to reconcile with measurements of $h$ from Hubble's law.  Another possibility is to reduce $n$ below the canonical value $n=1$. This `tilted spectrum' option has been widely investigated \\cite{will,LL1,tilt,natural2,gelb,LL2,berkeley,capri}, and it might be viable with $n\\simeq 0.7$. Unfortunately most inflation models with tilt also generate significant gravitational waves which ruin this concordance, as we discuss later. Of course one can combine the old universe and tilted spectrum options.  A third option is to change the hypothesis of completely cold dark matter, which reduces the small scale density perturbation because cold dark matter maximises its rate of growth. An attractive possibility, from both a theoretical and observational viewpoint, is to invoke a fraction $\\Omega_\\nu$ of hot dark matter in the form of massive neutrinos. This {\\it mixed dark matter} (MDM) model has been widely investigated \\cite{mdm,lymanalpha,davis,pogosyan,bobqaisar,silvio,mymnras,boblast,capri}, both with and without the option of allowing $h$ and $n$ to depart from their canonical values. We shall see that it may be observationally viable with $\\Omega_\\nu=0.15$ or so and the canonical $h$ and $n$. Other possibilities yet to be investigated fully are to replace the CDM by some form of warm dark matter like sterile neutrinos, or to replace it by decaying or self-interacting dark matter.  The final possibility is to reduce the matter density, either  with \\cite{lambda,both,tegsilkopen} or without \\cite{lowomega,both,tegsilkopen} a cosmological constant to keep the total energy density critical. In practice one takes the non-baryonic dark matter to be completely cold in that case. This {\\it low density CDM model} has been quite widely investigated and with $h$ and $n$ at their canonical values it may be observationally viable with $\\Omega_c$ of order $0.5$ or so.  All of this assumes that there is no significant gravitational wave contribution to the cmb anisotropy. A contribution up to 50\\% or so is not ruled out by present data, and is actually predicted by some models of inflation \\cite{LL1,paul,davesal}. Of the models that are well motivated from particle physics, those predicting a significant contribution also predict a spectral index $n<1$, and on the large scales explored by COBE they predict that the relative gravitational wave contribution to the mean square cmb anisotropy is $R\\simeq 6(1-n)$. In these models the normalization of the density perturbation is therefore reduced by a factor $[1+6(1-n)]\\mhalf$, and the possible existence of this factor should be taken into account when considering tilt in the spectral index. On the other hand, almost all inflation models suggest that if the spectral index is very close to 1 then the gravitational wave contribution will be negligible.  In this article the focus is on the (critical density) MDM model, which of course includes the critical density CDM model as a special case, allowing $h$ and $n$ to vary, and keeping in mind the possibility of gravitational waves. The low density CDM model will be mentioned only briefly, and other possibilities not at all. ",
        "conclusions": "To conclude, we have provided a review of the machinery required in order to translate an initial spectrum of density irregularities into a form amenable for fairly direct comparison with a range of observations. Although some of our discussion has wider application, we have focussed on the standard model of structure formation, which invokes an initially Gaussian, adiabatic, scale invariant density perturbation and more or less cold dark matter. It is at present the one under the most active consideration, because it is the simplest, and also because the required initial density perturbation might be generated as a vacuum fluctuation during inflation.  We have gone on to compare the standard model with presently available data, indicating the relative merits of altering the Hubble constant, tilting the primordial spectrum and incorporating a component of hot dark matter. All of these have been envisaged as ways to remedy the shortcomings of the canonical cold dark matter model.  Our treatment of the observations breaks new ground in that it combines for the first time several relatively new observational constraints. For the normalization of the spectrum from the COBE measurement of the cmb anisotropy, we use the most recent determination that has been provided by G\\'{o}rski and collaborators. It is significantly higher than earlier determinations. We assess carefully the uncertainty in the determination of the normalization on the scale $8h\\mone\\Mpc$ that comes from the cluster abundance, quantifying its dependence on the assumed cluster mass. We establish a simple and rather firm constraint from damped Lyman alpha systems at high redshift, which provide a powerful lower limit on some scale of order $0.1$ to $1\\Mpc$. Finally, on the basis of an earlier study \\cite{tegsilk} we make a preliminary estimate of the epoch of re-ionisation in the various models.  Our technique for comparing theory with observation is to look not at the power spectrum, but at the dispersion of the density contrast smoothed on a scale $R$. This has the great advantage of being closer to what is actually measured, while still being simple to calculate for a given theoretical model. Particularly when one normalises theories and observations to a benchmark model as in Figure 3, the comparison between theory and observation can be very clearly illustrated.  While present observations are strong enough to exclude the standard CDM model, they are not of sufficient quality to select amongst different ways of generalising it, particularly when one realises that if tilt or a hot component are to be varied then one must certainly also allow $h$ to vary in combination. It is clear from Figure 3 that these options are most cleanly probed by observations on scales from a few tens to a few hundreds of megaparsecs, and we should look forward to this region of the spectrum being probed by both small scale microwave anisotropy experiments and by larger scale galaxy correlation (and peculiar velocity) measurements."
    },
    "9408/hep-ph9408304_arXiv.txt": {
        "abstract": "The difficulties for non-standard solar models (NSSM) in resolving the solar neutrino problem are discussed stressing the incompatibility of the gallium--Kamiokande data, and of the gallium--chlorine data. We conclude that NSSM's cannot explain simultaneously the results of any two of the solar neutrino data (chlorine, Kamiokande and gallium). We address further the question whether the MSW solution exists for NSSM's (e.g. models with $^8$B neutrino flux much lower than the standard one and/or central temperature $T_c$ very different from $T_c^{\\text{SSM}}$). We demonstrate that the MSW solution exists and is very stable relative to changes of $S_{17}$ ($S$-factor for $p$ + $^7$Be reaction) and $T_c$. In particular, $\\Delta m^2$ is almost constant, while $\\sin^2 2\\theta$ depends on the exact values of $S_{17}$ (or $^8$B-neutrino flux) and $T_c$. ",
        "introduction": "\\label{intro} The standard solar model (SSM) gives a very good description of the Sun. An impressive confirmation of the SSM is given by helioseismological observations, which, according to Ref.~\\cite{Turck93a}, agree with the SSM predictions at the level of $0.5\\%$ for distances down to $0.2R_{\\odot}$. As a matter of fact there are at least 12 SSM's whose predictions are in reasonable agreement~\\cite{Bahcall88a,Lebreton88,Sackman90,Proffitt91,Guzik91,% Bahcall92a,Guenter92,Christi92,Ahens92,Bertomieu93,Turck93b,Cast93b}. All these models include the same physics, and the slight differences between their results are mostly caused by differences in the input parameters.  However, all SSM's predict neutrino fluxes which are in disagreement with the observations of all four neutrino experiments ~\\cite{Davis94a,Davis94b,Kamio,Gallex,SAGE} (see Table~\\ref{Exp}). This deficit of the detected solar neutrinos is referred to as the solar neutrino problem (SNP).  The SSM has uncertainties that basically reflect the uncertainties in the input parameters. It has been shown~\\cite{Cast93a,Cast94b,Hata94a,Hata94b} that the most important uncertainties in the neutrino fluxes can be described by three parameters, the central temperature $T_c$, the $S$-factor $S_{17}$ for the $^7\\text{Be} + p \\to {}^8\\text{B} + \\gamma$ cross section, and the ratio $S^2_{33}/S_{34}$ of the $S$-factors for the reactions $^3\\text{He} + ^3\\text{He} \\to ^4\\text{He} + 2p$ and $^3\\text{He} + ^4\\text{He}  \\to ^7\\text{Be} + \\gamma$. The uncertainty in the central temperature actually sums up uncertainties in the astrophysical factor $S_{11}$ for the $p+p \\to ^2\\text{He} + e^{+} + \\nu$  cross section, in the solar opacity, which depends in particular on the metal abundances $Z/X$ and on possible collective plasma effects~\\cite{Tsytovich}, in age of the Sun, and in some other quantities.  One can distinguish between SSM's and NSSM's. All SSM's consider the same physical processes, and use similar input parameters. On the contrary, NSSM's consider large changes of the input parameters, often outside their estimated uncertainties~\\cite{Cast94b}, and/or introduce new physical processes. In practice we assume that SSM's are characterized by the input parameters and their uncertainties as given in Ref.~\\cite{Cast94b}, which basically follows Bahcall~\\cite{Bahcall92a,Bahcall89}.  Recently two new developments have attracted a great deal of attention. If confirmed, they can change dramatically the prediction for the solar neutrino fluxes.  The first one is the measurement~\\cite{Moto94} of $S_{17}$ factor from the cross section of dissociation for the $^8$B nuclei in the Coulomb field of $^{208}$Pb: $^8\\text{B} + {}^{208}\\text{Pb} \\to {}^{208}\\text{Pb} + {}^7\\text{Be} + p $. The preliminary result gives $S_{17}= 16.7 \\pm 3.2$~eV~barn, which should be compared with the value $S_{17}= 24 \\pm 2$~eV~barn used by Bahcall and Pinsonneault~\\cite{Bahcall92a}. This new result would imply a proportional reduction of the predicted $^8$B neutrino flux, which would come close to the flux measured by Kamiokande.  The second new development consists in the theoretical consideration of collective plasma effects in the Sun. These effects have the potentiality of lowering the solar opacity by as much as 18\\%~\\cite{Tsytovich}, with the consequent lowering of the theoretical prediction of the Sun central temperature by $2\\div 3$\\%.  The previous considerations have motivated us to study NSSM's where both the astrophysical factor $S_{17}$ and the Sun central temperature are left almost as free parameters. As discussed in the next Section, this freedom, and even more so the aforementioned effects, are insufficient to resolve the SNP. It is possible to explain the observed $^8$B neutrino flux, i.e. the Kamiokande data, but it is not possible satisfy any two of the three experimental data (chlorine, Kamiokande and gallium) simultaneously. The basic reason for this failure is that the SNP affects now also the $^7$Be neutrinos, and not only the rare $^8$B neutrinos~\\cite{Cast94b,Bere94a,Bahcall94b}: the combination of the two gallium experiments with Homestake or Kamiokande, or the combination of Homestake with Kamiokande, implies a too low $^7$Be-neutrino flux. As concluded in Sect.~\\ref{noastro}, the astrophysical solution is strongly disfavored.  The MSW mechanism~\\cite{MSW78,MSW86} offers the attractive possibility of selective suppression of the $^7$Be neutrinos, and reconciling the SSM with experiments. After having examined the input parameter uncertainties and the NSSM's as possible solutions to the SNP, it is only fair to examine how they affect the MSW solution. In particular, we ask whether the MSW solution exists for values of $S_{17}$ and central temperature significantly different from the standard ones (the range of $S_{17}$ considered includes the new preliminary result: $S_{17}=11\\div23$~eV~barn~\\cite{Moto94}).  In Section~\\ref{MSW}, we shall demonstrate the validity of the MSW solution and its weak dependence on the input parameters. We find that considerable changes of the parameters $S_{17}$ and $T_c$ affect the mixing angle, but $\\Delta m^2$ remains practically the same. ",
        "conclusions": "\\label{conclu} For standard massless neutrinos the data of any two solar neutrino measurements (chlorine, Kamiokande and gallium) are incompatible. The incompatibility of the chlorine and Kamiokande data is a well recognized problem~\\cite{Bahcall90a,Bahcall93a,Cast93a,Hata94a,Bere94a,Bere93a}. The conflict between the gallium and Kamiokande data, and between the gallium and chlorine data, can be shown in different ways. One can obtain~\\cite{Bere94a} a rigorous model-independent lower limit for the gallium detector counting rate by neglecting the $^7$Be neutrino flux, using the observational lower limit for the $^8$B neutrino flux, and taking the flux of $pp$ neutrinos from the solar luminosity restriction. It gives $82.5$~SNU to be compared with the combined result of the two gallium experiments $74 \\pm 9$~SNU. Using the gallium data, the luminosity constraint, and the lower limit for the flux of $^8$B neutrinos from either Homestake or Kamiokande, one can derive~\\cite{Cast94b} a model-independent limit on the $^7$Be neutrino flux. The updated limit using the new gallium data~\\cite{Gallex,SAGE} is $1.9 \\times 10^9~\\text{cm}^{-2}\\text{s}^{-1}$ ($2\\sigma$), i.e. less than $40\\%$ of the SSM value. Most recently J.~N.~Bahcall~\\cite{Bahcall94b} found that the $^7$Be neutrino signal in a gallium detector is less than 19~SNU at the 95\\% C.L., about half of the 36~SNU predicted by the SSM.  We have demonstrated that there are no values of $S_{17}$ and $T_c$, the two most important solar-model parameters as neutrino fluxes are concerned, which satisfy the combination of any two experimental data out of three (chlorine, Kamiokande and gallium).  Nowadays, the essence of solar neutrino problem is the low $^7$Be neutrino flux. Nuclear/astrophysical solutions to the solar neutrino problem are strongly disfavored. The MSW mechanism offers a very attractive solution to the solar neutrino problem.  The new measurements of $S_{17}$ factor~\\cite{Moto94} and collective plasma effects~\\cite{Tsytovich} can considerably change the solar-model parameters $S_{17}$ and $T_c$. In fact, we might face what now are non-standard solar models, which are also incompatible with the solar neutrino data. Does the MSW solution exist for these models?  We have demonstrated that the MSW solution exists for NSSM's with parameters $S_{17}$ and $T_c$ within their realistic uncertainties, and beyond. Our conclusion concerning the $^8$B neutrino flux coincides with the results of Ref.~\\cite{Krastev94}. The MSW solution is stable in mass ($\\Delta m^2$) even if $S_{17}$ or $T_c$ are drastically changed (a change of $S_{17}$ practically results in only a proportional change of the $^8$B  neutrino flux). In particular, $\\Delta m^2$ is restricted to the range $ 4 (\\text{meV})^2<\\Delta m^2 < 12 (\\text{meV})^2$. The physical reason of this stability is the fact that the solar neutrino experiments observe most of the predicted flux of $pp$ neutrinos, and very small fraction of the $^7$Be neutrino flux.  Solar-model predictions for the $^8$B neutrino flux are only important for the determination of the mixing angle. Models with reduced $^8$B neutrino flux prefer the small angle solution, because of the stronger suppression of the $^7$Be/$^8$B flux ratio. The large angle solution disappears for models with reduced $^8$B neutrino flux. Large-mixing-angle solutions reappear in models with hotter core and/or larger $S_{17}$ factor, since they predict a $^8$B-neutrino-flux increase larger than the corresponding increase of the $^7$Be flux."
    },
    "9408/astro-ph9408091_arXiv.txt": {
        "abstract": "We report the discovery of a new catacysmic variable system, RXJ051541+0104.6. The optical spectrum has a blue continuum with superposed H~I and He~I and II emission lines. The soft X-ray spectrum is well fit with a 50~eV black body. The X-ray and optical data are suggestive of an AM~Herculis system. The X-ray light curve shows extreme variability on timescales of seconds, and suggests an orbital period of order 8~hours, nearly twice that of the longest catalogued AM~Her period. When bright, the X-ray light curve breaks up into a series of discrete bursts, which may be due to accretion of dense blobs of material of about 10$^{17}$~gm mass. ",
        "introduction": "As part of a program to study the spatial distribution of low mass pre-main sequence stars in the Orion OB1 association, we obtained the ROSAT PSPC observation RP200930. This image is centered at 5$^h$14$^m$24.0$^s$ +1$^o$42'0\" (J2000), to the west of the Ori~OB1a association, and was meant to serve as a control field, far from the region where we expected to find low mass association members. The standard SASS processing yielded 37 X-ray sources. In the course of obtaining optical spectra of the stellar counterparts of these X-ray sources, we discovered a previously unknown cataclysmic variable with extreme X-ray variability.  Cataclysmic variables are semi-detached binary systems, with accretion from a low mass non-degenerate star onto a white dwarf. The cataclysmic variables come in a number of classes, defined by accretion rates and accretion geometry (e.g., C\\'ordova 1993). Among these are the various types of novae and nova-like systems and the magnetized systems, the polars and intermediate polars. Polars and intermediate polars are often discovered by virtue of their X-ray emission.  The polars, or AM~Her systems (e.g., Cropper 1990), are strongly magnetized systems with the white dwarf rotating synchronously on the orbital period. There is no evidence for accretion disks in polars: the accretion is along magnetic field lines onto the magnetic poles of the white dwarf. Orbital periods are generally less than 2 hours, but have periods up to 4.6~hours (RXJ1313-32; Ritter \\& Kolb 1993). Polars are strong soft X-ray sources, and 20 such systems have been discovered in the ROSAT all-sky survey (e.g., Beuermann \\& Schwope 1994), more than doubling the previously-known population. The intermediate polars, or DQ~Her systems (e.g., Patterson 1994), are also magnetized, but the white dwarf periods are much shorter than the orbital periods, presumably because the magnetic fields are too weak to enforce synchronization. Accretion is through a disk. Periods tend to be longer than for the polars, and the X-ray emission tends to be dominated by a hard bremsstrahlung component.  This new cataclysmic variable exhibits several puzzling characteristics, which we discuss below. The X-ray light curve resembles that of a single-poled polar\\footnote{We use this term to describe a polar with an X-ray light curve similar to that of VV~Pup, where there are two magnetic poles but only the principle pole is occulted by the body of the white dwarf.}, yet the period is much longer than any known polar. The soft X-ray and optical spectra are more similar to those of polars than of intermediate polars. The X-ray emission is highly variable; when bright, the emission breaks up into a discontinuous series of discrete bursts. This behavior is unlike that seen in any cataclysmic variable discussed to date, but is expected if the accretion consists not of a smooth flow but of discrete blobs of material (e.g., Frank, King, \\& Lasota 1988). This object may provide clues to the evolution of cataclysmic variables, and the relation of the polars to the intermediate polars. ",
        "conclusions": "The optical and X-ray spectra, and the large $\\frac{f_X}{f_{V}}$ ratio suggest that this object is a magnetic cataclysmic variable (e.g., Mason 1985, Cropper 1990). The rapid X-ray variability requires a compact object. The relative strengths of the He~II $\\lambda$4686 and H$\\beta$ emission lines (Liebert \\& Stockman 1985), and the strength of the soft-X-ray emission, are suggestive of an AM~Her variable. The folded X-ray light curve, shown in Figure~2, is similar to the X-ray light curve of VV~Pup (Osborne \\etal 1984), though on a much longer period. The light curve shows that the quiescent interval lasts about half the period, followed by a smooth increase to a maximum about 7 times brighter than the quiescent level. We assume this period is the orbital period of the system. Based on the light curve, we consider it likely that this object is a polar or an intermediate polar wherein the principle accreting pole is occulted every stellar rotation.  No currently catalogued AM~Her system has a period longer than 4.6~hours (Ritter \\& Kolb 1993). If this is indeed an AM~Her system, with a synchronously-rotating white dwarf, then the magnetic field strength must be quite large to force circularization at an 8 hour orbital period. Using Patterson's (1994) scaling law, B must be of order 7$\\times$10$^8$G if the accretion rate and the mass of the white dwarf are typical of magnetic cataclysmic variables. Such a field strength, or even a considerably weaker field, should produce easily-visible circular polarization. If the white dwarf's rotation is not synchronous, then this object may represent the progenitors of an AM Her-type system. This object may provide some insights into the relation between the polars and the intermediate polars.  Recently, Garnavich \\etal (1994) reported that the system is an eclipsing magnetic cataclysmic variable, with a 7.98~hour orbital period. They estimated a magnetic field strength of up to 5.5$\\times$10$^{7}$~G from the strength of the cyclotron emission humps. This is fully consistent with our characterization based on the X-ray light curve. The magnetic field is weaker than predicted from Patterson's scaling law, suggesting that either the white dwarf is about half the mass of that in a typical magnetic cataclysmic variable, that the system is not in synchronous rotation, or that the scaling law breaks down for large separations.  The most unusual aspect of this object is the X-ray variability on short timescales. Figure~9 shows a segment of the active interval during RP200930. Note that the X-ray emission breaks up into a sequence of bursts with typical duration of 10 seconds. There is no evidence for a steady component underlying the bursts. The bursts are not periodic, but there is a mean separation time between them of order 30~seconds. These appear comparable to the quasi-periodic bursts seen in AM~Her by Tuohy \\etal (1981), although in AM~Her the bursts are superposed on a strong background. Short bursts have also been seen in BL~Hyi (Beuermann \\& Schwope 1989). The detected flux in the typical burst is 3$\\times$10$^{-9}$~erg~cm$^{-2}$, yielding a burst energy \\begin{center} E$_b~\\sim$~1.3$\\times$10$^{34}$~D$^2_{200}$~erg \\end{center} where D$_{200}$ is the distance to the source in units of 200~pc. The mass of the accreting blob, if all its kinetic energy is released in the soft X-rays, is \\begin{center}M$_{blob}$~=~1.0$\\times$10$^{17}$D$^2_{200}$R$_9$/M$_1$~gm, \\end{center} where R$_9$ and M$_1$ are the radius and mass of the white dwarf in units of 10$^9$~cm and one solar mass, respectively.  The soft blackbody component is generally thought to be attributable to thermal reprocessing of harder bremsstrahlung and cyclotron X-ray emission. The discrete bursts are suggestive of blobby accretion models developed by Kuijpers \\& Pringle (1982) and Frank \\etal (1988). The blobs possess sufficient ram pressure to plunge deep into the photosphere before shocking. The hard X-ray bremsstrahlung radiation suffers multiple scatterings and emerges as the soft blackbody component seen in many AM~Her systems (e.g., Lamb \\& Masters 1979).  We can estimate the mean mass accretion rate, $\\dot{\\rm m}$, and the fractional area, f, undergoing accretion by equating the blackbody luminosity \\begin{center}L$_{\\rm BB}$~=~4$\\pi$R$^2$f$\\sigma$T$^4$,\\end{center} the observed X-ray luminosity (dereddened and extrapolated over the entire wavelength range of the blackbody emission, using the spectral fit) \\begin{center}L$_X$~=~4$\\pi$d$^2$f$_x$,\\end{center} and the accretion luminosity \\begin{center}L$_{\\rm acc}$~=~GM$\\dot{\\rm m}$/R,\\end{center} where we assume that all the accretion luminosity is radiated into the blackbody component. Plugging in the observed temperature and observed X-ray flux, L$_{\\rm BB}$~=~7.5$\\times$10$^{37}$R$_9^2$f, L$_{X}$~=~7.5$\\times$10$^{31}\\frac{f_x}{<f_x>}$D$_{200}^2$, and L$_{\\rm acc}$~=~1.3$\\times$10$^{17}$M$_1\\dot{\\rm m}$/R$_9$. Rearranging these, we find that \\begin{center} f~=~1.0$\\times$10$^{-6}\\frac{f_x}{<f_x>}(\\frac{D_{200}}{R_9})^2$, and\\\\ $\\dot{\\rm m}$~=~5.8$\\times$10$^{14}\\frac{f_x}{<f_x>}$D$^2_{200}\\frac{R_9}{M_1}$~gm~s$^{-1}$, \\end{center} where $f_x$ and $<f_x>$ are the instantaneous and mean X-ray fluxes. For a typical luminosity of L$_{33}$~=~10$^{33}$erg~s$^{-1}$, \\begin{center} $\\frac{f_x}{<f_x>}$D$^2_{200}$=13.3L$_{33}$,\\\\ f~=~1.3$\\times$10$^{-5}$L$_{33}$R$_9^{-2}$, and \\\\ $\\dot{\\rm m}$~=~7.7$\\times$10$^{15}$L$_{33}$R$_9$/M$_1$ \\end{center} The instantaneous luminosity varies by nearly two orders of magnitude, but we see no evidence for significant changes in the temperature. Therefore, increases in luminosity must be due to increases in $\\dot{\\rm m}$ and f. Both scale linearly with the instantaneous flux. This suggests that all the blobs penetrate to sufficiently large optical depths to thermalize completely. The more massive blobs may penetrate deeper and illuminate a larger fraction of the surface area.  The wide binary orbit can accomodate a relatively luminous secondary. The Na~D absorption (Figure~7), coupled with the lack of strong TiO absorption bands, suggests a secondary with a G to late-K spectral type. The Na~D absorption could be partly interstellar, but are the strongest metallic features in the red in G-K stars; our spectrum is too noisy to detect the $\\lambda$6495\\AA\\ blend. The colors observed on 1993 December 5 are fairly red, but are not consistent with any cool star. If the secondary has the colors of a normal dwarf, and the light is the sum of the secondary and a blue continuum, then the secondary cannot be earlier than about spectral type K2. Garnavich \\etal (1994) obtained an M0 spectral type for the secondary from a spectrum during eclipse.  This system provides strong evidence for accretion through discrete blobs. In this system the blobby accretion may not be just sporadic, as has been seen in other polars, but may be the normal state. Accretion is not expected to produce a smooth hydrodynamic flow, and larger separation between components may give more time for the instabilities to grow and to produce better-defined blobs than in the shorter-period systems. If the fraction of the accreting matter in discrete blobs is large, as suggested by the X-ray light curve, then the hard X-ray flux from this object should be minimal.  In conclusion, RXJ051541+0104.6 is a magnetic cataclysmic variable with a period over twice as long as the longest known AM~Her system. Further studies may reveal much about both the accretion processes in close binaries and the evolution of cataclysmic variable systems."
    },
    "9408/astro-ph9408017_arXiv.txt": {
        "abstract": "In recent years there has been a developing realization that the interesting large--scale structure of voids, ``pancakes\", and filaments in the Universe is a consequence of the efficacy of an approximation scheme for cosmological gravitation clustering proposal by Zel'dovich in 1970.  However, this scheme was only supposed to apply to smoothed initial conditions.  We show that this can be explained by the fact that the gravitationally evolved potential from N--body simulations closely resembles the smoothed potential of the initial conditions.  The resulting ``hierarchical pancaking\" picture effectively combines features of the former Soviet and Western theoretical pictures for galaxy and large--scale structure formation. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9408/astro-ph9408003_arXiv.txt": {
        "abstract": " ",
        "introduction": "In this paper I compare several different methods for determining the spectral index $n$ of the power spectrum of primordial density perturbations.  All of the determinations that use {\\it COBE} data are statistically compatible with the $n \\approx 1$ predicted by the inflationary scenario.  Because the largest scales appear as large angular scale features on the finite solid angle of sky that is available for viewing, the statistical uncertainties in the determination of $n$ cannot be conquered by the usual expedient of getting more data. A careful consideration of the statistical methods used to analyze the large-angular scale {\\it COBE} data is needed. ",
        "conclusions": "In conclusion, both the {\\it COBE}\\, $\\Delta T$ data alone and the ratio of the {\\it COBE}\\, $\\Delta T$ data to $1^\\circ$ scale $\\Delta T$ are consistent with the $n \\approx 1$ prediction of the inflationary scenario.  Furthermore, the implied level of gravitational potential perturbations is sufficient to produce the observed large scale (100 Mpc) structure if both the $n = 1$ and $\\Omega = 1$ predictions of inflation are correct, and the Universe is dominated by Dark Matter.  \\begin{table}[t] \\begin{center} \\begin{tabular}{|llcll|} \\hline Method & COBE dataset & Q? & Result & Reference \\\\ \\hline Correlation function & 1 year 53$\\times$90 & N & $n_{app} = 1.15^{+0.45}_{-0.65}$ & Smoot {\\it etal} ('92) \\\\ COBE\\,:\\,$\\sigma_8$      & 1 year 53+90        & N & $n_{pri} = 1 \\pm 0.23 $ & Wright {\\it etal} ('92) \\\\ Genus \\vs\\ smoothing & 1 year 53           & Y & $n_{app} = 1.7^{+1.3}_{-1.1}$ & Smoot {\\it etal} ('94)  \\\\ RMS \\vs\\ smoothing   & 1 year 53           & Y & $n_{app} = 1.7^{+0.3}_{-0.6}$ & Smoot {\\it etal} ('94)  \\\\ Correlation function & 2 year 53$\\times$90 & Y & $n_{app} = 1.3^{+0.49}_{-0.55}$ & Bennett {\\it etal} ('94) \\\\ Correlation function & 2 year 53$\\times$90 & N & $n_{app} = 1.1^{+0.60}_{-0.55}$ & Bennett {\\it etal} ('94) \\\\ COBE\\,:\\,$1^\\circ$ scale & 2 year NG           & N & $n_{pri} = 1.15\\pm 0.2$ & Wright {\\it etal} ('94) \\\\ Cross power spectrum & 2 year 53 \\& 90 & N & $n_{app} = 1.25^{+0.40}_{-0.45} $  & Wright {\\it etal} ('94) \\\\ Cross power spectrum & 2 year 53 \\& 90 & Y & $n_{app} = 1.39^{+0.34}_{-0.39} $  & \\\\ Orthonormal functions & 2 year 53+90 & N & $n_{app} = 1.02 \\pm 0.4 $ & G\\'orski {\\it etal} ('94) \\\\ COBE\\,:\\,$\\sigma_{100}$ & 1 year 53 & Y & $n_{pri} = 1.0 \\pm 0.16 $ & Peacock \\& Dodds \\\\ \\hline \\end{tabular} \\end{center} \\caption{Spectral index determinations} \\label{ntable} \\end{table}"
    },
    "9408/astro-ph9408102_arXiv.txt": {
        "abstract": " ",
        "introduction": " ",
        "conclusions": "BBN has the potential of providing among the strongest existing constraints on various types of dark matter.  It already provides the most compelling evidence against the existence of a closure density of baryonic dark matter.  Whether it is compatible with even a galactic halo density of baryons depends crucially on our ability to infer primordial light element abundances with less uncertainty than presently exists.  As has been shown, if uncertainties on $^4$He, D, and $^7$Li can be reduced, BBN could essentially fix the baryonic abundance in the universe, and constrain a great deal of other ``dark matter\" physics beyond the standard model. Nevertheless, the fact that systematic uncertainties dominate at present does not block our ability to make statistically meaningful statements. Also, as time proceeds and more independent observations are made we will undoubtedly get a better handle on the uncertainties which presently limit the efficacy of BBN constraints.  Until then, the tables and relations presented here should allow individuals to translate their own limits on the light element abundances into meaningful bounds on $N_{\\nu}$ and $\\etaten$.  \\bigskip I would like to thank Peter Kernan for his many essential contributions to the results presented here, and also David Schramm and Terry Walker for useful comments about various issues. Finally, I want to thank the organizers of the UCLA meeting for making it so exciting and pleasant.  \\vskip 0.1in \\noindent{\\bf References}"
    },
    "9408/astro-ph9408044_arXiv.txt": {
        "abstract": " ",
        "introduction": "\\indent  In many models of the very early universe, the canonical Einstein-Hilbert gravitational action emerges only as a low-energy effective theory, rather than being assumed from the start.~\\cite{adler}  A large class of these generalized Einstein theories (GETs) involves scalar fields non-minimally coupled to the Ricci curvature scalar.  Such Brans-Dicke-like couplings~\\cite{bd61} arise, for example, in models of superstring compactification~\\cite{string} and Kaluza-Klein theories~\\cite{freund}, and are related, via conformal transformation, to quantum-gravitational counter-terms, which are proportional to the square of the Ricci scalar.~\\cite{hirai}~\\cite{renorm} \\\\ \\indent  Recent experimental determinations of the power spectrum of density perturbations~\\cite{exp}, modeled as $\\cal{P} \\rm \\propto \\it k^{n_s} \\rm$~\\cite{physrep}, offer a rare glimpse of such Planck-scale physics.  The spectral index for this scalar perturbation, $n_s$, functions as a test for models of the very early universe, independently of the familiar test based on the magnitude of perturbations.  It has been shown, for example, that one well-known GET model of inflation, extended inflation~\\cite{EI}, cannot produce the observed nearly scale-invariant (Harrison-Zel'dovich) spectrum:  extended inflation predicts $n_s \\leq 0.76$, instead of $n_s = 1.00$.~\\cite{lidlyth92}  The constraints on $n_s$ for extended inflation come from that model's incorporation of a first order phase transition to exit inflation (see~\\cite{bubble} for more on this so-called \\lq $\\omega$ problem'.) As discussed in~\\cite{Spect}, this pitfall can be avoided in GET models of inflation which undergo a second order phase transition to exit the inflationary phase.  In this paper, three cousin-models of extended inflation are considered, all of which fare much better in comparisons with the observed values of $n_s$. \\\\ \\indent  The analysis is carried out to second order in the potential-slow-roll approximation (PSRA) parameters identified by Andrew Liddle, Paul Parsons, and John Barrow~\\cite{psra}, who have recently amended earlier work by several authors~\\cite{StewLyth}~\\cite{relating}. These papers are based on the Hamilton-Jacobi equations of motion for a theory with a scalar field minimally coupled to the curvature scalar; before they can be applied to the non-minimally coupled GETs considered here, use must be made of a conformal transformation~\\cite{hirai}~\\cite{conftrans}, which, via field redefinitions, puts the GET equations of motion into the \\lq\\lq Einstein frame\" form of an Einstein-Hilbert gravitational action with a minimally coupled scalar field. \\\\ \\indent  In this connection, it is important to keep Redouane Fakir and Salman Habib's cautionary note in mind. In~\\cite{FakHab} they have demonstrated that ambiguities arise when studying the quantum fluctuations of scalar fields in GETs in various frames: the scalar two-point correlation function evaluated in the \\lq\\lq Jordan\" or \\lq\\lq physical\" frame, in which the non-minimal $\\phi^2 R$ coupling is explicit, differs from the two-point correlation function evaluated after the field redefinitions, in the Einstein frame.  Yet, as discussed below, when the inflationary expansion is quasi-de Sitter, $a(t) \\propto \\exp(Ht)$, with $\\dot{H} \\simeq 0$, the ambiguities isolated in~\\cite{FakHab} affect the {\\it magnitude} of the correlation function only, and not the $k$-dependence (and hence not $n_s$; see eq. (58) in~\\cite{FakHab}).  All three of the models considered below display such quasi-de Sitter expansion under \\lq\\lq chaotic inflation\" initial conditions, and thus the Einstein frame formalism employed here for $n_s$ should remain unproblematic.  \\\\ \\indent  However, under \\lq\\lq new inflation\" initial conditions, two of the models evolve as a quasi-power-law, $a(t) \\propto t^p$. In these cases, ambiguities similar to those discussed in~\\cite{FakHab} {\\it do} affect the form of $n_s$.  As discussed below in section 3.2, the discrepancy between values of $n_s$ as calculated in the Jordan and Einstein frames arises because the curvature perturbation upon which the PSRA formalism is based, ${\\cal R} = (H / \\dot{\\phi}) \\> \\delta \\phi$~\\cite{physrep}~\\cite{StewLyth}, is not invariant with respect to the conformal transformation.  (This discrepancy can be resolved by choosing a suitable generalization of ${\\cal R}$; see~\\cite{DKpre}.) Still, it can be shown that even in these cases of quasi-power-law expansion, the numerical results for $n_s$ in the Jordan frame, as calculated with the PSRA formalism, differ negligibly from the Einstein frame results. \\\\ \\indent  The specific method for calculating $n_s$ is developed in section 2.  In section 3, the formalism is applied to induced-gravity inflation, for which we can compare the Einstein-frame results with Jordan-frame calculations.  In sections 4 and 5, the analysis is presented for two models with a different non-minimal $\\phi^2 R$ coupling and two different potentials.  Concluding remarks follow in section 6. \\\\ ",
        "conclusions": "\\indent  The three closely-related GET models of inflation considered above all predict values of $n_s$ close to the observed, nearly-scale-invariant spectrum of perturbations.  For the quasi-power-law cases (new inflation initial conditions), the spectral index varies roughly linearly with the non-minimal coupling constant $\\xi$, with negative slope.  For large values of $\\xi$, then, this negative slope-dependence of $n_s$ on $\\xi$ could drag the predictions for $n_s$ below the experimentally observed values.  Yet sufficient inflation requirements place stringent restrictions on $\\xi \\ll 1$; if such sufficient inflation requirements can be met, then the resulting spectral index deviates only little from $n_s = 1.00$.  In the quasi-de Sitter expansion cases (chaotic inflation initial conditions), $n_s$ again varies roughly linearly with $\\xi$, but with positive slope; $n_s$ thus remains close to $n_s = 1.00$ for most values of $\\xi$. Note that these small deviations of $n_s$ from the Harrison-Zel'dovich spectrum mean that each of the models considered here predicts very small values for the tensor-mode perturbation index, $n_T$, and the ratio of tensor to scalar mode amplitudes, $R$:  both $n_T$ and $R$ are proportional to $\\epsilon$ to first order~\\cite{psra}, and in each of the cases above, $0 < \\epsilon < \\left|\\eta\\right| \\ll 1$. \\\\ \\indent  Under new inflation initial conditions, the Einstein frame formalism employed here yields different forms of $n_s (\\xi)$ from calculations conducted exclusively in the Jordan frame.  The physical basis for these discrepancies is discussed in section 3.2, and is further treated in~\\cite{DKpre}.  However, again owing to the requirements from sufficient inflation, in the allowed regions of $\\xi$-space the numerical values for $n_s$ differ negligibly between the two frames.  Under chaotic inflation initial conditions, there are no discrepancies between the forms of $n_s (\\xi)$ in the two frames. \\\\ \\indent  Each of these models is able to produce acceptable spectra, even though their cousin-model extended inflation cannot, because they avoid {\\it both} of the so-called \\lq $\\omega$ problems' which plagued extended inflation.~\\cite{bubble}~\\cite{lidlyth92}~\\cite{Spect}  First, each of the models considered here exits inflation by slowly rolling towards the vacuum expectation value of its potential, thereby avoiding the strict requirements from bubble nucleation and percolation associated with a first order phase transition.  This means that there is no lower bound on $\\xi$ for these models. Second, by exiting inflation, all three of these models {\\it also} exit the GET phase:  after inflation, as $\\phi$ settles in to $v$ (or $0$, for the $\\lambda \\phi^4$ model), the coefficient of the Ricci scalar in the action, eq. (1), becomes the constant $1/(2\\kappa_N^2)$.  Thus, the second order phase transition responsible for ending inflation simultaneously delivers the universe into the canonical Einstein-Hilbert gravitational form.  Unlike extended inflation, then, present-day tests of Brans-Dicke gravitation versus Einsteinian general relativity place no restrictions on allowed values of $\\xi$ during the early universe. \\\\ \\indent  The approach used in this paper can be generalized further, by choosing a more general form for the GET action, eq. (1).  For example, specifically \\lq\\lq stringy\" effective actions, which often have the \\lq\\lq wrong\" sign for the kinetic term in eq. (1) and different effective scalar potentials~\\cite{string}, can be studied, as can models with more than one scalar field coupled to the Ricci scalar (e.g.,~\\cite{hybrid}). By studying these GET models of inflation with the methods employed here, we may further take advantage of the window on Planck scale physics offered by the primordial spectrum of density perturbations. \\\\"
    },
    "9408/astro-ph9408099_arXiv.txt": {
        "abstract": " ",
        "introduction": "In a paper uneagerly published in 1936, Einstein (1936) described how the apparent luminosity of a star may be temporarily amplified by the gravitational field of a second star that crosses close to the line of sight to the first. He concluded that the effect was of no practical interest. Half a century later, Paczy\\'nski (1986) revised Einstein's conclusion by noting that the search for microlensing events in the direction of the {\\it Large Magellanic Cloud} (LMC) may resolve the question of the extent to which the mass of the dark Halo of our galaxy is due to {\\it Brown-Dwarfs,} stars too faint to be readily observed otherwise.  The EROS (Aubourg {\\it et al.} 1993) and MACHO (Alcock {\\it et al.} 1993) collaborations have reported ``microlensing'' events of the expected characteristics in the direction of the LMC, and the MACHO (Alcock {\\it et al.} 1994) and OGLE (Udalski {\\it et al.} 1994) groups have seen similar events in the direction of the {\\it ``Galactic Bulge'',} centrally located in the Milky Way. In spite of the currently low statistics, the observers have established that the temporal shape, achromaticity, location in the Hertzsprung-Russell diagram, and non-repetitive character of the events place them far away from the tails of the distributions inferred from the observed variable stars. The events are either due to a novel and most implausible type of variable, whose properties are ``just so'' as to fool the observer, or to microlensing by the faint interlopers that one is searching for.  We are primarily interested in Brown-Dwarfs, {\\it compact objects} that act as gravitational lenses but that may otherwise be directly observable, with considerable toil, only at infrared wavelengths (Kerins \\& Carr 1994). Not to shine at visible frequencies, Brown-Dwarfs must be {\\bf lighter} than the thermo-nuclear ignition threshold, which for a compact object predominantly made of H and He is $m_{max}\\sim 0.085 M_\\odot$ (Graboske \\& Grossman 1971). Not to have evaporated during the age of the Galaxy, these bodies must be {\\bf heavier} than $(10^{-6}$-$10^{-7}) M_\\odot$ (De R\\'ujula, Jetzer and Mass\\'o 1992).  There is a cutoff on the mass of Brown-Dwarfs more stringent than the evaporation limit: the {\\it ``Jeans''} mass $m_{min}\\sim 7\\times 10^{-3} M_\\odot$ (Low \\& Lynden-Bell 1976), the lowest mass of a detached H/He gas-cloud fragment whose self-gravitational collapse into a compact object is not prevented by the developing thermal pressure. Although the Jeans limit is not absolute (Jupiter, Saturn, Uranus and Neptune are counterexamples to it), the relatively long durations of the observed microlensing events indicate that the objects responsible for them are in the upper domain of allowed masses, the question of a precise lowest-mass cutoff appears to be rather moot. We shall consequently restrict our considerations to compact objects whose masses range from the Jeans mass to the hydrogen-burning threshold. On-going observations are sensitive to microlensing by objects with masses lying anywhere in this mass range.   The existence of a dark halo in spiral galaxies is decisively demonstrated by their observed rotation curves. The nature of the constituents of this dark mass, contrary-wise, is debatable and debated. An important role in the discussion is played by constraints on the universal average ``baryonic'' density, stemming from the relative abundances of primordial elements that are inferred, after significant corrections, from spectral observations (Walker {\\it et al.} 1991). Recent measurements of the $^2$H abundance in distant intergalactic clouds (Songaila {\\it et al.} 1994, Carswell {\\it et al.} 1994) favour the conclusion that most baryonic matter is visible and accounted for, leaving no room for a predominantly  (baryonic) Brown-Dwarf constituency of our Halo.  Often used as an argument against a Halo made of Brown-Dwarfs is the contention that the density of all other stellar distributions falls off with distance from the galactic centres significantly faster than $\\sim r^{-2}$, the behaviour required to explain a flat rotation curve. But Sackett {\\it et al.} (1994) have recently observed that the Halo of the spiral NGC5907, though very dim, has a luminosity distribution that traces its dark mass.   In our opinion, it is too early to accept as conclusive the arguments favouring a baryonic or non-baryonic composition of galactic halos. We discuss the direct search for Brown-Dwarfs in the Halo of the Galaxy, if only because failure to find them in significant amounts would constitute the most intriguing observational result: it would strongly advocate for a Halo consisting of a substance more subtle than the ones we are made of.  The interest of Brown-Dwarfs would transcend stellar physics, should they significantly contribute to the Halo dark mass. Thus the spirit in which we shall discuss the microlensing data: Brown-Dwarfs in the Galaxy's Halo will be considered the ``signal'', dim lensing bodies from other stellar populations will be regarded as ``backgrounds''.  Various locations for these backgrounds have been discussed: the {\\it Thin Disk}, the {\\it Thick Disk} (Gould, Miralda-Escud\\'e \\& Bahcall 1994) and the {\\it Spheroid} (Giudice, Mollerach \\& Roulet 1994), all of them stellar populations extending beyond the location of our own solar system. Though we are immersed in these stellar distributions, the contribution of their unseen astral bodies to microlensing in the direction of the Magellanic Clouds was once thought to be quite negligible, relative to the full signal of a Brown-Dwarf-dominated Halo. But, if the dark constituency of these galactic components is sizable, they may significantly contribute to the LMC and SMC lensing rates. They could even account for the observations (Gould, Miralda-Escud\\'e \\& Bahcall 1994, Giudice, Mollerach \\& Roulet 1994) that, within very poor statistics, seem to fall short of the expected Halo rates. Dim objects in the LMC itself may also contribute to the microlensing of LMC stars.  To visualize the invisible, we show in  Fig. 1 contour plots of the different galactic dark-mass distributions that we shall discuss. The $x$ and $y$ axis are in the galactic plane,  the $y$ axis digs into the figure. For each population, the inner and outer contours correspond to volume densities of $10^{-2} M_\\odot/\\mbox{pc}^3$ and $10^{-3} M_\\odot/\\mbox{pc}^3$. The solar position is at ($-8.5$,\\, 0,\\, 0) kpc. The densest and most convenient microlensing target-fields of source stars are the Magellanic Clouds and the galactic Bulge. The LMC, assesing its distance from us to be $55$ kpc, is at (0,\\, $-$46,\\, $-$29) kpc. The SMC, reckoned to be located at $65$ kpc, is at (17,$-$39,$-$45) kpc. The galactic Bulge fills the central 1--2 kpc. We devote Section 2 to a detailed discussion of the spatial distributions of visible and dark mass in our Galaxy and in the LMC.  In this paper we discuss simple strategies to analyse microlensing data of modest statistics. We combine the modelling of various signal and background stellar populations with the information reflected in the first few moments (De R\\'ujula, Jetzer \\& Mass\\'o 1991) of the event-duration distribution: the number of events (the ``zeroth'' moment); the average duration $\\langle T \\rangle$; and the time dispersion $\\Delta T/T\\equiv \\sqrt{\\langle T^2\\rangle -\\langle T\\rangle^2}/\\langle T\\rangle$. The mass function of the lenses (number of objects per unit mass interval) is unknown apriori, and the predictions for the various duration moments depend on its assumed functional form. We deal with this problem by ``sweeping'' our results over the very large domain of mass-function ansatze discussed in Section~3.  In Section 4 we recall the basic expressions for the microlensing rate as a function of event duration, in the divers viewing directions of interest, and for the various lensing populations. In Section 5 we develop a feeling for the results by discussing ideal observations of single-mass lensing objects. In Section 6 we discuss realistic limited-statistics observations of objects whose mass function and location are unknown. We illustrate the effects of the detection efficiency as a function of event duration. This is not always possible, since only OGLE has already published the relevant information and MACHO is currently analysing the problem in detail\\footnote{ We are indebted to Pierre Bareyre for discussions on the EROS efficiencies.}.  The microlensing predictions corresponding to the Halo signal and the various possible backgrounds can be conveniently visualized by plotting the event rate and the event time-dispersion against the mean event duration. For observations in the direction of the Magellanic Clouds, even after the ``blurring'' induced by the apriori ignorance of the lensing-objects' mass function, the signal and backgrounds occupy distinct regions of these plots. It is therefore quite conceivable that, as the statistics improves to a few dozen events, the data favour one of these regions and the culprit microlensing star population can be pinned down. This is our main result, which will be reflected in Figs.~4 and 5. The comparison of SMC and LMC observations would also help locating the lensing agents.  In the direction of the Bulge the microlensing observables predicted for the different dark populations overlap to some extent, once the ignorance of the lensing mass function is duly taken into account. Thus, our proposed procedure to select the stellar distribution to which the microlensing objects belong should work for the LMC, but not for the Bulge. There the situation is even more challenging for, as is almost always the case in astronomy, the observations have spoiled the simplicity of the original picture.  The Bulge event rates reported by the OGLE and MACHO collaborations are larger than expected in any simple Brown-Dwarf scenario. And the event durations are surprisingly long. The observed rate can be brought to agree with theory by combining the contributions of several stellar populations. But the rate and the event durations cannot be simultaneously described by any combination of the conventional Halo, Disk and Spheroid dark-matter models (plus the contribution of faint Disk stars). To quantify the severity of this problem, and given the scarcity of the data, we must resort to a Kolmogorov--Smirnov test of the time distribution. We conclude that the disagreements are serious enough to justify modifications of ere accepted models of the inner galactic realm. Our analysis and some of these modifications (Alcock {\\it et al.} 1994, Paczy\\'nski {\\it et al.} 1994) are specified in Section 6d.  The titles and subtitles of Sections 2--6 image the organization of the paper. In the conclusions of Section 7 we fail to be truly conclusive, for our current understanding of galaxies is still modest, and the microlensing observations are still infants. ",
        "conclusions": "Microlensing observations are the best current tool to search for compact lumps of baryonic dark-matter in the Galaxy. The observational campaigns were designed to ascertain the extent to which the galactic Halo consists of massive astrophysical objects or, by exclusion, of a more elusive substance. Infrared searches, that we have not discussed, are another tool to locate nearby individual Brown Dwarfs, or their collective glow in another galaxy.  It is becoming increasingly clear that the microlensing observations are sensitive to ``backgrounds'' of dark objects residing in galactic components other than the Halo, such as the Spheroid and the Thick or Thin Disks. We have presented a detailed description of the microlensing Halo signal and the various backgrounds, an analysis designed to accomodate the foreseeable scarcity of data. Our aim is to pin down the likely location of the lensing objects, as well as to extract the first indications of what their mass function may be.  The observations of the Bulge are intriguing. We have analysed the statistical significance of the discrepancy between the OGLE observations and the expectations for simple dark-mass models and known faint stars, or combinations thereof. In agreement with previous authors (Alcock {\\it et al.}, 1994; Paczy\\'nski {\\it et al.} 1994), we conclude that the earlier understanding of the inner galactic realm must be revised. In this connection, microlensing observations with a good sensitivity for short-duration events (10 days or less), for which the expected rates are large, would be very useful. So would the comparison of observations in ``windows'' located at different latitudes and relative angles to the galactic centre.  Needless to emphasize, even a Brown-Dwarf-dominated galactic Halo would contribute very little to microlensing of Bulge stars, so that observations in that direction are not decisive to the question of the Halo constituency, though they constitute a handle on various microlensing ``backgrounds''.   We have argued that for the microlensing of LMC stars, the comparison of data and expectations for the rate, mean event duration and time dispersion should suffice to disentangle the galactic component to which the Brown-Dwarfs belong. A comparison of LMC and SMC rates may also come in handy.  To summarize, microlensing observations of the galactic Bulge are already significantly contributing to our astrophysical lore; very soon observations of the Magellanic Clouds ought to add to our knowledge of cosmology. The question of the nature of the Halo of our galaxy is still wide open, but the prospects for continuing progress appear to be excellent."
    },
    "9408/astro-ph9408094_arXiv.txt": {
        "abstract": " ",
        "introduction": "While the existence of dark matter is now firmly established, however, despite decades of herculean efforts, its nature remains as elusive as ever. Indeed it is  plausible that there is more than one type of dark matter, so that different types of dark matter dominate on different length scales. In this paper, we will focus on the smallest scale in the problem: the galactic halo scale, and address the following two questions about halo dark matter: (1) What fraction of dark matter in the  halo is in the form of  baryonic cold gas?  and (2) How is this gas distributed in the halo? We will show how   measurements of the diffuse gamma-ray background can lead to a quantitative understanding of both questions. Our study is motivated by recent suggestions that the halo dark matter may consist of  dense molecular clouds (Pfenniger, Combes and Martinet 1994; Pfenniger \\& Combes 1994; Gerhard \\& Silk 1994).  Several recent papers have discussed the idea of using the diffuse gamma ray flux to constrain the fraction of halo diffuse gas (Gilmore 1994; De Paolis et al. 1994). In this paper, we use  a detailed gamma-ray production function and two models of cosmic ray distribution to obtain a more accurate estimate of the diffuse gamma ray flux from baryonic gas. Furthermore, a   multipole expansion of the diffuse gamma ray background is developed with the aim of  exploring the possibility of detecting the flattening of  halo gas distribution by measuring the multipole moments of  the gamma ray background. ",
        "conclusions": ""
    },
    "9408/hep-ph9408208_arXiv.txt": {
        "abstract": "Astrophysical implications of neutrino mass and mixings are discussed. The status of solar and atmospheric neutrino problems, and recent developments concerning nuclear physics input to solar models and solar opacities are reviewed. Implications of neutrino mass and mixings in supernova dynamics are explored. The effects of supernova density fluctuations in neutrino propagation is described. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9408/astro-ph9408095_arXiv.txt": {
        "abstract": " ",
        "introduction": "Valuable information about the  early universe and  the physical processes that generate the primordial fluctuations from which  cosmic structure formed can be gained from measurements of cosmic microwave background radiation (CBR) temperature anisotropies (White, Scott \\& Silk 1993).  An especially important issue is the Gaussian nature of the temperature anisotropies. Gaussianity in the linear regime is a generic conswequence of most inflationary theories for the origin   of the fluctuations. However none of these models fare particularly well at accounting for the large-scale power spectrum of density fluctuations on all observed scales, and rather extreme solutions have been advocated  (e.g. Peacock and Dodds  1994; Peebles 1994; Bartlett, Blanchard, Turner and Silk 1994). Hence deviations from Gaussianity are a possibility that can only be limited by experiment. Although significant progress has been made in the understanding of the CBR since the  detection of fluctuations at $7^{\\circ}$ angular scale by the COBE satellite (Bennett et al. 1992; Smoot et al. 1992; Wright et al. 1992),  the Gaussianity question remain unresolved.   Despite the full-sky coverage achieved by COBE, the combination of   beam smoothing and the effects of cosmic variance  (Luo 1994; Hinshaw et al. 1994) preclude  COBE alone from testing Gaussianity.  At the same time, while the detection of degree-scale fluctuations intrinsic to the CBR  is a remarkable achievement, the datasets at these intermediate angular scales are still too small to carry out Gaussianity tests,   although tests at these angular scales would certainly be  decisive once large sky coverage is achieved (Coulson et al. 1994).   Despite all these difficulties, there are non-Gaussian imprints on the CBR sky that are within the grasp of current on-going experiments. A clear non-Gaussian signature would be the detection of   point-like sources. In fact, two candidates for such sources may have been detected by the medium scale anisotropy measurement (MSAM) experiment.  There are serious issues of data analysis that pertain to whether or not possible  point sources are subtracted before attempting to measure temperature fluctuations: we do not address such issues here. Rather, we ask the question: could possible foreground sources produce point source-like signals in a CBR experiment at MSAM resolution and frequency?   Various topological defects, notably soft-domain wall bubbles (Goetz \\& N\\\"{o}tzold 1991; Turner et al. 1991), the global monopoles (Bennett \\& Rhie 1991) or texture (Turok \\& Spergel 1991) are capable of producing spotlike CBR anisotropies of any  desired size by choosing appropriate model parameters. However, before relying on topological defects as the interpretation of candidate sources, one has to carefully filter out any foregrounds. In carrying out the experiments, CBR anisotropy signals have to be separated carefully from  local foreground sub-millimeter and millimeter radiation fields. Three possible foreground sources are studied in this paper. These are cold dust clouds, nonthermal extragalactic radio sources and the Sunyaev-Zeldovich effect  in foreground galaxy clusters. Multifrequency measurements  have previously been studied as a ttechnique for  removing the foreground (Brandt et al. 1994), with a focus on the point-like sources listed above.  The arrangement of this paper is as follows: an effective spectral index for point sources is introduced in section 2, and  results for radio sources, dust clouds and the SZ effect are presented and discussed in section 3. We conclude that both radio sources and the SZ effect are ruled out as a possible explanation of MSAM-type sources, that is to say, several $sigma$ fluctuations that are point-like at $\\sim30$ arc-min resolution and have a spectral energy distribution that, crudely at least, is indistinguishable from that of the CBR. Cold dust emission remains a possibility, but we find that this option  also may be  ruled out if a conventional value for the dust emissivity $\\alpha = 1.5 \\pm 0.5$ is adopted. ",
        "conclusions": ""
    },
    "9408/astro-ph9408018_arXiv.txt": {
        "abstract": "We analyse the large--scale velocity field obtained by N--body simulations of cold dark matter (CDM) models with non--Gaussian primordial density fluctuations, considering models with both positive and negative primordial skewness in the density fluctuation distribution. We study the velocity probability distribution and calculate the dependence of the bulk flow, one--point velocity dispersion and Cosmic Mach Number on the filtering size. We find that the sign of the primordial skewness of the density field provides poor discriminatory power on the evolved velocity field. All non--Gaussian models here considered tend to have lower velocity dispersion and bulk flow than the standard Gaussian CDM model, while the Cosmic Mach Number turns out to be a poor statistic in characterizing the models. Next, we compare the large--scale velocity field of a composite sample of optically selected galaxies as described by the Local Group properties, bulk flow, velocity correlation function and Cosmic Mach Number, with the velocity field of mock catalogues extracted from the N--body simulations. The comparison does not clearly permit to single out a best model: the standard Gaussian model is however marginally preferred by the maximum likelihood analysis. ",
        "introduction": "The cornerstone of current theories of structure formation in the universe is the dominance of a non--baryonic dark matter component. During the last decade the standard cold dark matter (hereafter SCDM) scenario has shown a high predictive power in explaining many observed properties of the large--scale galaxy distribution: the constituents of dark matter in this model are massive particles, which decoupled when non relativistic or have never been in thermal equilibrium; the primordial perturbations are assumed to be Gaussian and adiabatic with a scale--invariant power--spectrum, $P(k) \\propto k^n$, with $n=1$ (the so--called Harrison--Zel'dovich spectral index); the SCDM scenario is also characterized by an Einstein--de Sitter universe with vanishing cosmological constant. The amplitude of the primordial perturbations is usually parametrised by the linear {\\it bias} factor $b$, defined as the inverse of the {\\it rms} mass fluctuation on a sharp--edged sphere of radius $8~h^{-1}$ Mpc (in this work we will adopt the value $h=0.5$ for the Hubble constant $H_0$ in units of $100$ km ${\\rm s}^{-1} {\\rm Mpc}^{-1}$). The {\\it COBE} DMR detection of large angular scale anisotropies of the cosmic microwave background (Smoot et al 1992; Bennett et al. 1994) can be used to fix the normalization of the model, leading to $b \\approx 1$. This normalization makes the model completely specified.  However, it is well known that this model presents some serious problems, mostly due to the high ratio of small to large--scale power: in particular, the {\\it COBE} normalization implies excessive velocity dispersion on Mpc scale (e.g. Gelb \\& Bertschinger 1994) and is unable to reproduce the slope of the galaxy angular correlation function obtained from the APM survey (Maddox et al. 1990).  To overcome these difficulties many alternatives to this basic model have been proposed: $i)$ ``tilted\" (i.e. $n < 1$) CDM models (Vittorio, Matarrese \\& Lucchin 1988; Adams et al. 1992; Cen et al. 1992; Lucchin, Matarrese \\& Mollerach 1992; Tormen et al. 1993, Moscardini et al. 1994), $ii)$ hybrid (i.e. hot plus cold) dark matter models (e.g. Klypin et al. 1993, and references therein), $iii)$ CDM models with a relic cosmological constant (e.g. Efstathiou, Bond \\& White 1992, and references therein), $iv)$ non--Gaussian CDM models (hereafter NGCDM; Moscardini et al. 1991; Messina et al. 1992).  In the present work we consider the last alternative. Physical motivations for this class of models can be given in terms of the effect of relic topological defects (e.g. Scherrer \\& Bertschinger 1991; Scherrer 1992, and references therein), or in terms of the inflationary dynamics of models containing multiple scalar fields (see e.g. Salopek 1992), or in the frame of the cosmic explosion scenario (e.g. Weinberg, Ostriker \\& Dekel 1989). NGCDM models have been investigated in a series of papers (Moscardini et al. 1991; Matarrese et al. 1992; Messina et al. 1992; Coles et al. 1993a,b; Moscardini et al. 1993; Borgani et al. 1994), mainly devoted to the analysis of the clustering properties of the matter distribution on large scales, as resulting from N--body simulations. A similar analysis was done by Weinberg \\& Cole (1992), who, however, performed numerical simulations with scale--free initial power--spectra. Of course, the ultimate probe of the non--Gaussian character of the primordial perturbation field can only be obtained from the analysis of the cosmic microwave background (CMB) anisotropies on large angular scales: a number of statistical tests have been recently proposed in order to detect possible non--Gaussian signatures, such as the skewness of the temperature distribution (Hinshaw et al. 1994) and the genus of iso--temperature contours (Smoot et al. 1994). The analyses performed on the first year {\\em COBE} data have revealed that non--Gaussian signals are not present on the angular scales probed by the DMR experiment ($\\magcir 7^\\circ$), beyond those due to the effects of the cosmic variance (e.g. Scaramella \\& Vittorio 1991). The implication of this result is that non--Gaussian features cannot be relevant for the large--scale gravitational potential, so, either the primordial fluctuations were indeed Gaussian, or primordial non--random phases were only present on scales below $7^\\circ$, as it seems the case for anisotropies generated by topological defects (e.g. Coulson et al. 1994, and references therein). Therefore, for the models we consider here, we just have to require that the gravitational potential was significantly non--Gaussian already at redshifts of order of a tenth, when we start to evolve our system, and up to scales as large as $\\sim 10^2$ Mpc (much below the {\\em COBE} scale), as probed by our simulations.  This work is devoted to a detailed study of the velocity field in N--body simulations of NGCDM models, and to a comparison of the large--scale velocity field of a composite sample of optically selected galaxies (1184 galaxies, with known radial peculiar velocities, grouped in 704 objects, from the ``Mark II\" compilation), with that obtained from the simulations. In particular, we calculate the probability to reproduce the observed properties of the Local Group and the observed values for the bulk flow, the velocity correlation function, and the Cosmic Mach Number of the data in mock catalogues extracted from our simulations. A similar analysis has been performed by Tormen et al. (1993) and Moscardini et al. (1994) in the frame of open and/or tilted CDM models. Contrary to most previous analyses of NGCDM models (Moscardini et al. 1991; Messina et al. 1992), we here fix the `present time' of the simulations in such a way that the linear bias parameter $b$ is one, consistently with the {\\em COBE} normalization\\footnote{Even though the statistical analysis of CMB anisotropies on large angular scales for non--Gaussian models cannot be reduced to calculating the {\\em rms} fluctuation we assume here that the effect of non--Gaussian statistics on the {\\em COBE} DMR scale is small, so that we can safely use the standard normalization, leading to $b\\approx 1$.}. The same choice for the normalization has been made by Moscardini et al. (1993), where the effect of primordial non--random phases on the large--scale behaviour of the galaxy angular two--point function has been investigated: it was found that models with initially negatively skewed fluctuations are in principle capable of reconciling the lack of large--scale power of the CDM spectrum with the observed clustering of APM galaxies.  The plan of the paper is as follows. In Section 2 we introduce our skewed CDM models. In Section 3 we discuss the general properties of the velocity field of the simulations, analysing the bulk flow, the one--point velocity dispersion and the Cosmic Mach Number at different smoothing scales. We also analyse the density and velocity probability distributions and power--spectra. Section 4 is instead devoted to the statistical comparison of mock catalogues extracted from the simulations with observational data. Conclusions are drawn in Section 5. ",
        "conclusions": "In this paper we have analysed the large--scale velocity field in the context of non--Gaussian CDM models. Weinberg \\& Cole (1992) partially analysed the properties of peculiar velocities in their non--Gaussian models, assuming scale--free initial conditions. Our work presents the first detailed study of large--scale motions as resulting from primordial non--random phases in a CDM scenario.  Unlike previous analyses on the same models, mostly devoted to the study of the matter distribution and its clustering properties, in this work we found that the sign of the primordial skewness of the density field provides a poor discriminatory power. All our non--Gaussian models tend to have lower velocity dispersion and bulk flow than the standard Gaussian CDM model. We interpret this as due to the effect of primordial phase correlation which, in skew--positive models, causes power to be transferred from large scales (important for velocities) to small scales, whereas in skew--negative models it causes a general slowing down of the growth of the power--spectrum at all scales. This result is different to our earlier findings due to the different normalization here applied, which is dictated by the {\\em COBE} data, i.e. $b\\approx 1$.  In particular, this choice does not allow our skew--negative models to fully develop their dynamical properties, discovered in previous studies, where it was found that only after a lengthy evolution these models could achieve the right slope for the correlation function, assumed to indicate the ``present time\". These non--Gaussian models, therefore, only experience moderate non--linear evolution (as shown by the low value of $\\sigma_\\delta$ in Table 1), which makes their large--scale velocity field still sensitive to the initial conditions (i.e. to the CDM power--spectrum) and only marginally dependent, through mildly non--linear effects, on its primordial kurtosis and on the skewness of the density fluctuations. This very fact implies that the comparison of our non--Gaussian models with observational data does not clearly permit to single out a best model: the standard Gaussian model is marginally preferred by the maximum likelihood analysis.  Moreover, these results suggest that, contrary to naive expectations, primordial non--random phases do not help in producing large--scale bulk motions such as those indicated by the Lauer \\& Postman (1994) analysis, which is one of the most challenging observational results for the present structure formation scenarios."
    },
    "9408/hep-ph9408282_arXiv.txt": {
        "abstract": "The tau neutrino with a mass of about 10 MeV can be the ``late decaying particle'' in the cold dark matter scenario  for the formation of structure in the Universe. We show how this may be realized specifically in the recently proposed doublet Majoron model. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9408/astro-ph9408015_arXiv.txt": {
        "abstract": "\\noindent The meaning of the inflationary slow-roll approximation is formalised. Comparisons are made between an approach based on the Hamilton-Jacobi equations, governing the evolution of the Hubble parameter, and the usual scenario based on the evolution of the potential energy density. The vital role of the inflationary attractor solution is emphasised, and some of its properties described. We propose a new measure of inflation, based upon contraction of the comoving Hubble length as opposed to the usual $e$-foldings of physical expansion, and derive relevant formulae. We introduce an infinite hierarchy of slow-roll parameters, and show that only a finite number of them are required to produce results to a given order. The extension of the slow-roll approximation into an analytic slow-roll {\\em expansion}, converging on the exact solution, is provided. Its role in calculations of inflationary dynamics is discussed. We explore rational-approximants as a method of extending the range of convergence of the slow-roll expansion up to, and beyond, the end of inflation. ",
        "introduction": "Inflationary universe models are based upon the possibility of slow evolution of some scalar field $\\phi$ in a potential $V(\\phi)$ \\cite{KT,LL93}. Although some exact solutions of this problem exist, most detailed studies of inflation have been made using numerical integration, or by employing an approximation scheme. The `slow-roll approximation' \\cite{ST,SB90,LL92}, which neglects the most slowly changing terms in the equations of motion, is the most widely used. Although this approximation works well in many cases, we know that it must eventually fail if inflation is to end. Moreover, even weak violations of it can result in significant deviations from the standard predications for observables such as the spectrum of density perturbations or the density of gravitational waves in the universe \\cite{SL93,LL93}. As observational data sharpen, it is important to derive a suite of predictions for the observables that are as accurate as possible, and which cover all possible inflationary models.  In the literature, one finds two different versions of the slow-roll approximation. The first \\cite{ST,LL92} places restrictions on the form of the potential, and requires the evolution of the scalar field to have reached its asymptotic form. This approach is most appropriate when studying inflation in a specific potential. We shall call it the {\\em Potential Slow-Roll Approximation}, or PSRA. The other form of the approximation places conditions on the evolution of the Hubble parameter during inflation \\cite{CKLL}. We call this the {\\em Hubble Slow-Roll Approximation}, or HSRA. It has distinct advantages over the PSRA, possessing a clearer geometrical interpretation and more convenient analytic properties. These make it best suited for general studies, where the potential is not specified.  In this paper, we clarify the meaning of the different slow-roll approximations that exist in the literature, which often describe a variety of slightly different approximation schemes applied to different variables at different orders. By formalising the slow-roll approximation in detail, we will show how to use it as the basis of a {\\em slow-roll expansion} --- a sequence of analytic approximations which converge to the exact solution of the equations of motion for an inflationary universe. Such a technique relies strongly on the notion of the inflationary attractor, whose properties we describe. The use of Pad\\'{e} and Canterbury approximants \\cite{BAK,PTVF} allows us to further improve the range and rate of convergence of this slow-roll expansion. ",
        "conclusions": "\\label{conc} \\setcounter{equation}{0}  By defining a suitable hierarchy of parameters, we have extended the slow-roll approximation to a slow-roll expansion, allowing progressively more accurate {\\em analytic} approximations to be constructed via an order-by-order decomposition in terms of slow-roll parameters. The use of rational approximants pushes the range of validity of the slow-roll expansion up to, and in many instances beyond, the end of inflation. With the accurate observational information becoming available, this allows an assessment of the accuracy of calculations within the slow-roll approximation, and is especially important with the present considerable emphasis focussed on inflationary models which make predictions far from the standard (zeroth-order) case.  We have used these parameters to define an improved measure of the amount of inflation. However, present uncertainties regarding the physics of reheating make it useful only in rather extreme circumstances such as a temporary suspension of inflation, during which the universe remains scalar field dominated, as in the hybrid inflation model of Ref.~\\cite{RLL}.  Let us caution the reader regarding the necessity of the attractor condition for the slow-roll expansion to make sense. By incorporating order-by-order corrections, we can only generate one solution, $H(\\phi)$, out of the one-parameter family of actual solutions allowed by the freedom of $H$, or equivalently $\\dot{\\phi}$), permitted by the initial conditions. If the attractor hypothesis is not satisfied, then the solution generated --- while conceivably an accurate particular solution of the equations of motion --- need have no relation to the actual dynamical solutions which might be attained. A case in point is the exact `intermediate' inflation solution \\cite{M90,B90,BL93}. For small $\\phi$, this solution corresponds to the rather unnatural (and noninflationary) behaviour of the field moving up the potential and over a maximum, beyond which inflation starts. If one attempts to use our procedure to describe this entrance to inflation, the solutions generated bear no particular resemblance to the exact solution until well into the inflationary regime\\footnote{By contrast, the `intermediate solution' can also be employed as the slow-roll solution in the simple potential $V \\propto \\phi^{-\\beta}$ (with $\\beta$ and $\\phi$ both positive), where the attractor hypothesis can be applied, though the solution to which the expansion process tends would have to be found numerically again.}. This serves as a cautionary note, that known exact solutions are typically only late-time attractors, and unless a significant period of inflation occurs {\\em before} the time of interest, so that the attractor solution is reached, they are of little relevance.  Importantly, with regard to the exit from inflation, we are on much safer ground. It is assumed that enough time has passed for the attractor to be reached, and hence all solutions exit from inflation in the same way. Therefore, when our expansion procedure supplies a particular solution, it provides an excellent description of the way in which the entire one parameter family of initial conditions will exit inflation. Without this vital point, the generation of solutions via the slow-roll expansion would be fruitless.  We have concentrated on the dynamics of inflation, rather than on the perturbation spectra produced from them. However, the slow-roll expansion can also be brought into play there; as an example, we quote the results for the spectral indices $n$ for the density perturbations and $n_T$ for the gravitational waves (see \\cite{LL93} for precise definitions). These have long been taken as approximately $1$ and $0$ respectively; results to first-order were given by Liddle and Lyth \\cite{LL92} and to second-order by Stewart and Lyth \\cite{SL93}. With our definitions, these read in the HSRA and PSRA respectively \\begin{eqnarray} 1-n & = &  4 \\epsilon_{{\\scriptscriptstyle H}} - 2 \\eta_{{\\scriptscriptstyle H}} + 2(1+c) \\epsilon_{{\\scriptscriptstyle H}}^2 + \\frac{1}{2} (3 - 5c) \\epsilon_{{\\scriptscriptstyle H}} \\eta_{{\\scriptscriptstyle H}} - \\frac{1}{2}(3-c) \\xi_{{\\scriptscriptstyle H}}^2 + \\cdots \\,; \\\\ & = &  6 \\epsilon_{{\\scriptscriptstyle V}} - 2 \\eta_{{\\scriptscriptstyle V}} -\\frac{1}{3}(44-18c) \\epsilon_{{\\scriptscriptstyle V}}^2 - (4c-14) \\epsilon_{{\\scriptscriptstyle V}} \\eta_{{\\scriptscriptstyle V}} - \\frac{2}{3} \\eta_{{\\scriptscriptstyle V}}^2 -\\frac{1}{6} (13-3c)\\xi_{{\\scriptscriptstyle V}}^2 \\nonumber \\\\ & & \\mbox{} + \\cdots \\,; \\\\ n_T & = &  -2 \\epsilon_{{\\scriptscriptstyle H}} -(3+c)\\epsilon_{{\\scriptscriptstyle H}}^2 + (1+c) \\epsilon_{{\\scriptscriptstyle H}} \\eta_{{\\scriptscriptstyle H}} + \\cdots \\,; \\\\ & = &  -2 \\epsilon_{{\\scriptscriptstyle V}} -\\frac{1}{3}(8+6c) \\epsilon_{{\\scriptscriptstyle V}}^2 + \\frac{1}{3} (1+3c) \\epsilon_{{\\scriptscriptstyle V}} \\eta_{{\\scriptscriptstyle V}} + \\cdots \\,, \\end{eqnarray} where $c = 4(\\ln 2 + \\gamma)$ with $\\gamma$ being Euler's constant. Notice the factors in $1-n$ change even at first-order, due to the different definitions of $\\eta$ which have been used. Similarly, we reproduce the second-order result for the ratio $R$ of tensor and scalar amplitudes \\cite{SL93} \\begin{eqnarray} R & = & \\frac{25}{2}\\epsilon_{\\scriptscriptstyle H} \\left[1 + 2c\\left(\\epsilon_{\\scriptscriptstyle H} - \\eta_{\\scriptscriptstyle H} \\right) +\\cdots \\right] \\\\ & = & \\frac{25}{2}\\epsilon_{\\scriptscriptstyle V} \\left[1 + 2\\left(c - \\frac{1}{3} \\right) \\left( 2\\epsilon_{\\scriptscriptstyle V} - \\eta_{\\scriptscriptstyle V} \\right) +\\cdots \\right] \\end{eqnarray} though it should be noted that this is not a direct observable \\cite{LT94}. Unlike the relatively simple dynamics which we have emphasised in this paper, no way of extending these expressions analytically to arbitrary order is known.  \\vspace*{12pt} \\noindent {\\em Final note:} As we were completing this paper we received a preprint by Lidsey and Waga \\cite{LW94} which also discusses the slow-roll approximation, although with a considerably different emphasis."
    },
    "9408/hep-ph9408386_arXiv.txt": {
        "abstract": "We show that present experiments imply that neutrinos are nonstandard at the 87\\% C.L., independently of solar or nuclear physics. Moreover, if neutrinos are standard, the $^7$Be flux must be almost zero. Even if we arbitrarily disregard one of the experiments, the neutrino flux must still be less than half of the value predicted by standard solar models. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9408/astro-ph9408034_arXiv.txt": {
        "abstract": " ",
        "introduction": "A central concept for particle physics theories attempting to unify the fundamental interactions is the concept of symmetry breaking. This symmetry breaking plays a crucial role in the Weinberg-Salam standard electroweak model ( Masiero 1984) whose extraordinary success in explaining electroweak scale physics reaches a  precision rarely found before in other areas of science (Koratzinos 1994). In the context of the standard Big Bang cosmological theory the spontaneous breaking of fundamental symmetries is realized as a phase transition in the early universe. Such phase transitions have several exciting cosmological consequences thus providing an important link between particle physics and cosmology.  A particularly interesting cosmological issue is the origin of structure in the universe. This structure is believed to have emerged by the gravitational growth of primordial matter fluctuations which are superposed on the smooth background required by the cosmological principle, the main assumption of the Big Bang theory.  The above mentioned link of cosmology to particle physics theories has led to the generation of two classes of theories which attempt to provide physically motivated solutions to the problem of the origin of structure in the universe. According to the one class of theories, based on inflation, primordial fluctuations arose from zero point quantum fluctuations of a scalar field during an epoch of superluminal expansion of the scale factor of the universe. These fluctuations may be shown to obey Gaussian statistics to a very high degree and to have an approximately scale invariant power spectrum.  According to the second class of theories, those based on topological defects, primordial fluctuations were produced by a superposition of seeds made of localized energy density trapped during a symmetry breaking phase transition in the early universe. Topological defects with linear geometry are known as cosmic strings and may be shown to be consistent with standard cosmology unlike their pointlike (monopoles) and planar (domain walls) counterparts which require dilution by inflation to avoid overclosing the universe. Cosmic strings are predicted to form during a phase transition in the early universe by many but not all Grand Unified Theories (GUTs).  The main elegant feature of the cosmic string model that has caused significant attention during the past decade is that the only free parameter of the model (the effective mass per unit length of the wiggly string $\\mu$ ) is fixed to approximately the same value from two completely independent directions. {}From the {\\it microphysical} point of view the constraint $G\\mu\\simeq (m_{GUT}/m_P)^2 \\simeq 10^{-6}$  is imposed in order that strings form during the physically realizable GUT phase transition. {}From the {\\it macrophysical} point of view the same constraint arises by demanding that the string model be consistent with measurements of Cosmic Microwave Background (CMB) anisotropies and that fluctuations are strong enough for structures to form by the present time. This mass-scale ratio for $G\\mu$ is actually a very attractive feature and even models of inflation have been proposed (Freese et al. 1990, Dvali et al. 1994) where observational predictions are related to similar mass scale relations.  Cosmic strings can account for the formation of large scale filaments and sheets (Vachaspati 1986; Stebbins et al. 1987; Perivolaropoulos, Brandenberger \\& Stebbins 1990; Vachaspati \\& Vilenkin 1991; Vollick 1992; Hara \\& Miyoshi 1993), galaxy formation at epochs $z\\sim 2-3$ (Brandenberger et al. 1987) and galactic magnetic fields (Vachaspati 1992b). They also generate peculiar velocities on large scales (Vachaspati 1992a; Perivolaropoulos \\& Vachaspati 1993), and are consistent with the amplitude, spectral index (Bouchet, Bennett \\& Stebbins 1988; Bennett, Stebbins \\& Bouchet 1992; Perivolaropoulos 1993a; Hindmarsh 1993) and the statistics (Gott et al. 1990; Perivolaropoulos 1993b; Moessner, Perivolaropoulos \\& Brandenberger 1993; Coulson et al. 1993; Luo 1994) of the CMB anisotropies measured by COBE on angular scales of order $\\theta\\sim 10^\\circ$.  Strings may also leave their imprint on the CMB mainly in three different ways. The best studied mechanism for producing temperature fluctuations on the CMB by cosmic strings is the Kaiser-Stebbins effect (Kaiser \\&  Stebbins 1984; Gott 1985). According to this effect, moving long strings present between the time of recombination $t_{rec}$ and today produce (due to their deficit angle (Vilenkin 1981)) discontinuities in the CMB temperature between photons reaching the observer through opposite sides of the string. Another mechanism for producing CMB fluctuations by cosmic strings is based on potential fluctuations on the last scattering surface (LSS). Long strings and loops present between the time of equal matter and radiation $t_{eq}$ and the time of recombination $t_{rec}$ induce density and  velocity fluctuations to their surrounding matter. These fluctuations grow gravitationally and at $t_{rec}$ they produce potential fluctuations on the LSS. Temperature fluctuations arise because photons have to climb out of a potential with spatially dependent depth. A third mechanism for the production of temperature anisotropies is based on the Doppler effect. Moving long strings present on the LSS drag the surrounding plasma and produce velocity fields. Thus, photons scattered for last time on these perturbed last scatterers suffer temperature fluctuations due to the Doppler effect.  It was recently shown (Perivolaropoulos 1994) how, by superposing the effects of these three mechanisms at all times from $t_{rec}$ to today, the power spectrum of the total temperature perturbation may be obtained. It turns out that (assuming standard recombination) both Doppler and potential fluctuations at the LSS dominate over post-recombination effects on angular scales below $2^\\circ$. However this is not the case for very large scales (where we will be focusing in the present paper) and this justifies our neglecting the former two sources of CMB anisotropies. The main effect of these neglected perturbations is an increase of the gaussian character of the fluctuations on small angular scales.  The main assumptions of the model were explained in (Perivolaropoulos 1993a). Here we will only review them briefly for completeness. As mentioned above, discontinuities in the temperature of the photons arise due to the peculiar nature of the spacetime around a long string which even though is {\\it locally} flat, {\\it globally} has the geometry of a cone with deficit angle $8\\pi G\\mu$. Several are the cosmological effects produced by the mere existence of this deficit angle (Shellard 1994), e.g., arcsecond-double images from GUT strings at redshifts $z\\sim 1$, flatten structures from string wakes or elongated filamentary structures from slowly moving long wiggly strings and, of more relevance in our present work, post-recombination CMB anisotropy (White, Scott and Silk 1994) string induced effects (Kaiser \\& Stebbins 1984).  The magnitude of the discontinuity is proportional not only to the deficit angle but also to the string velocity $v_s$ and depends on the relative orientation between the unit vector along the string ${\\hat s}$ and the unit photon wave-vector ${\\hat k}$. It is given by (Stebbins 1988) \\begin{equation} {{\\Delta T}\\over T}=\\pm 4\\pi G\\mu v_s \\gamma_s {\\hat k} \\cdot ({\\hat v_s}\\times {\\hat s}) \\end{equation} where $\\gamma_s$ is the relativistic Lorentz factor and the sign changes when the string is crossed. Also, long strings within each horizon have random velocities, positions and orientations.  We discretize the time between $t_{rec}$ and today by a set of $N$ Hubble time-steps $t_i$ such that $t_{i+1} = t_i \\, \\delta $, i.e., the horizon gets multiplied by $\\delta $ in each time-step. For $z_{rec}\\sim 1400$ we have $N \\simeq \\log_{\\delta}[(1400)^{3/2}]$.  In the frame of the multiple impulse approximation the effect of the string network on a photon beam is just the linear superposition of the individual effects, taking into account compensation (Traschen et al. 1986; Veeraraghavan \\& Stebbins 1990; Magueijo 1992), that is, only those strings within a horizon distance from the beam inflict perturbations to the photons.  In the following section we show how to construct the general q-point function of CMB anisotropies at large angular scales produced through the Kaiser-Stebbins effect. Explicit calculations are performed for the four-point function and its zero-lag limit, the kurtosis. Next, we calculate the (cosmic) variance for the kurtosis assuming Gaussian statistics for arbitrary value of the spectral index and compare it with the string predicted value (section 3). Finally, in section 4 we briefly discuss our results.  \\vspace{18pt} ",
        "conclusions": "In the present paper we showed how to implement the multiple impulse approximation for perturbations on a photon beam (stemming from the effect of the string network) in the actual construction of higher order correlations for the CMB anisotropies. We then focused on the four-point function and on the excess kurtosis parameter, finding for the latter a value ${\\cal K}\\sim 10^{-2}$.  We also calculated explicitly the rms excess kurtosis ${\\cal K}_{CV}$ predicted to exist even for a Gaussian underlying field and showed its dependence on the primordial spectral index of density fluctuations. This constitutes the main source of theoretical uncertainty at COBE scales. In fact, the cosmic string signature that might have been observable is actually blurred in the cosmic variance mist reigning at very large scales.  Nevertheless, there is still a chance of getting a string-characteristic angular dependence from the study of the mean four-point correlation function by exploiting the particular geometries deriving from it; namely, its collapsed cases (where some of the five independent angles are taken to be zero) or from particular choices for these angles (as in the case of taking all angles equal).  A preliminary analysis (Gangui \\& Perivolaropoulos 1994) making use of just one non-vanishing angle in a collapsed configuration as the one mentioned above shows a potentially interesting effect that could eventually increase notably the small non-Gaussian signal, and suggests that this is indeed a subject worth of further investigation. Some of these alternatives are presently under study and we expect to report progress on this subject in a future publication.  \\vspace{5mm} \\noindent{\\bf Acknowledgements:} It is a pleasure to thank A. Masiero and Q. Shafi for instructive discussions, and for having made this collaboration possible by inviting one of us (L.P.) to lecture in the ICTP summer school. A.G. wants also to acknowledge S. Matarrese and D.W. Sciama for encouragement, and R. Innocente and L. Urgias for their kind assistance with the numerical computations. This work was supported by the Italian MURST (A.G.) and by a CfA Postdoctoral fellowship (L.P.).  \\vspace{18pt}"
    },
    "9408/hep-ph9408321_arXiv.txt": {
        "abstract": "Gravitino produced in the inflationary universe are studied. When the gravitino decays into a neutrino and a sneutrino, the emitted high energy neutrinos scatter off the background neutrinos and produce charged leptons (mainly electrons and positrons), which cause the electro-magnetic cascades and produce many soft photons.  We obtain the spectra of the high energy neutrinos as well as the spectrum of the high energy photon by integrating a set of Boltzmann equations.  Requiring these photons should not alter the abundances of the light elements (D, $^3$He, $^4$He) in the universe, we can set the stringent upperbound on the reheating temperature after the inflation. We find that $T_R \\lesssim (10^{10}-10^{12})$GeV for $m_{3/2}\\sim (100\\GEV - 1\\TEV)$, which is more stringent than the constraints in the previous works. ",
        "introduction": "\\label{introduction}  \\hspace*{\\parindent} In models based on supergravity~\\cite{NPB212-413}, it has been pointed out that there exist some light particles whose interactions are suppressed by powers of the gravitational scale $M = M_{Pl}/\\sqrt{8\\pi} \\simeq 2.4\\times 10^{18}\\GEV$.  Such particles have nothing to do with collider experiments, but may affect the standard scenario of big-bang cosmology~\\cite{PRL48-1303,NPB277-556,PLB131-59}. The gravitino, which is the gauge field associated with local supersymmetry (SUSY), is one of the weakly interacting particles in supergravity models, and we expect that the mass of the gravitino is of order of typical SUSY-breaking scale.  Since the gravitino has only gravitational interaction with other particles, its lifetime is very long even if it is unstable. In standard cosmology, the gravitino with mass $m_{3/2}\\sim$ $O$(100GeV -- 10TeV) is excluded since it decays after the big-bang nucleosynthesis (BBN) and produces an unacceptable amount of entropy, which conflicts with the predictions of BBN~\\cite{PRL48-1303}. We may avoid this constraint by assuming the inflationary cosmology, in which the initial abundance of the gravitino is diluted by the exponential expansion of the universe~\\cite{PLB118-59}.  However gravitinos are reproduced by scattering processes off the thermal radiation after the universe has been reheated. Since the number density of the secondary gravitino is proportional to the reheating temperature, upperbound on the reheating temperature should be imposed not to overproduce gravitinos~\\cite{PLB127-30} -- \\cite{KMI}.  In the recent paper~\\cite{KMI}, we consider the unstable gravitino which decays into photon ($\\gamma$) and photino ($\\tilde{\\gamma}$) and derive upperbound on the reheating temperature $T_R$ ($T_R \\lesssim 10^6\\GEV$ for $m_{3/2} \\sim 100\\GEV$, $T_R \\lesssim 10^{9}\\GEV$ for $m_{3/2} \\sim 1\\TEV$) by requiring the produced high energy photons should not alter the abundances of light elements synthesized in BBN. The above constraint seems to be very stringent since such low reheating temperature requires very small decay rate of the inflaton field. For example, in chaotic inflation with a inflaton whose interactions are suppressed by gravitational scale $M$, the inflaton decay rate is expected to be $\\Gamma_{inf} \\sim m_{inf}^3/M_{Pl}^2$ with $m_{inf}$ being the inflaton mass, and hence the reheating temperature is estimated as\\cite{Kolb-Terner} \\beq T_R \\sim 0.1\\sqrt{\\Gamma_{inf}M_{Pl}} \\sim 10^{9}\\GEV, \\label{tr} \\eeq requiring that the inflaton field should produce the density perturbations observed by COBE ($m_{inf} \\sim 10^{13}\\GEV$)~\\cite{PRL69-3602}.  However the constraints might become much weaker when the gravitino decays only into weakly interacting particles. In the particle content of the minimal SUSY standard model, the only candidates are neutrino and sneutrino.  In this letter, we assume that the gravitino decays only into a neutrino and a sneutrino and derive constraints on the reheating temperature. In this case, the emitted high energy neutrino may scatter off the background neutrino and produce an electron-positron (or muon-anti-muon) pair, which then produces many soft photons through electro-magnetic cascade processes and destruct the light elements.  Since the interaction between high energy neutrinos and background neutrinos is weak, it seems that the destruction of the light elements is not efficient.  In fact, Gratsias, Scherrer and Spergel~\\cite{PLB262-198} showed that the constraint is not so stringent for the case that the gravitino decays into a neutrino and a sneutrino.  However the previous analysis seems to be incomplete in a couple of points.  First Gratsias et.al.~\\cite{PLB262-198} totally neglect the secondary high energy neutrinos which are produced by neutrino-neutrino scattering. The effect of the secondary neutrino may be important for heavy gravitino ($m_{3/2} \\gtrsim 1$TeV).  Second, they only study the case where the destruction of $^4$He results in the overproduction of $(^3{\\rm He} + {\\rm D})$. However, for the heavy gravitino which decays in early stage of the BBN, the destruction of D is more important since the electro-magnetic cascade process is so efficient that the energy of soft photons becomes less than the threshold of $^4$He.  Furthermore, as pointed out in ref.\\cite{KMI}, the previous estimation of the gravitino production in the reheating epoch is underestimated. Those effects which are not taken into account in ref.\\cite{PLB262-198} may lead to more stringent constraint on the reheating temperature.  Therefore, in this letter, we reexamine the decay of the gravitino into a neutrino and a sneutrino ($\\psi_{\\mu} \\rightarrow \\nu + \\tilde{\\nu}$) with taking all relevant effect into account, and as a result, we have obtained more stringent upperbound on the reheating temperature. ",
        "conclusions": "\\label{sec:results}  \\hspace*{\\parindent} The allowed regions that satisfy the observational constraints (\\ref{obs-he4})--(\\ref{obs-h23}) is shown in the $m_{3/2}-T_R$ plane in Fig.\\ref{fig:const}. In Fig.\\ref{fig:const} one can see that for the gravitino with mass between $\\sim$ 100GeV and $\\sim$ 1TeV, the overproduction of ${\\rm D}$ and $^3{\\rm He}$ gives the most stringent constraint, while the upperbound on the reheating temperature is determined from the destruction of D for $m_{3/2} \\simeq (1-3)$TeV. Notice that D destruction is not considered in the previous work~\\cite{PLB262-198}.  Furthermore the constrain from $({\\rm D} + ^3{\\rm He})$ overproduction is more stringent. The reasons why we obtain the more stringent constrain are i) the gravitino abundance is (4--5) times higher than the one obtained in ref.\\cite{PLB145-181} that the previous authors used, ii) the secondary neutrinos are taken into account in our calculation, and iii) the gravitino lifetime for $\\psi_{\\mu} \\rightarrow \\nu + \\tilde{\\nu}$ is longer by a factor 2 than the lifetime for $\\psi_{\\mu} \\rightarrow \\gamma + \\tilde{\\gamma}$. (In ref.\\cite{PLB262-198} it is presumed that $\\Gamma_{3/2}(\\psi_{\\mu} \\rightarrow \\nu +\\tilde{\\nu}) = \\Gamma_{3/2}(\\psi_{\\mu} \\rightarrow \\gamma + \\tilde{\\gamma})$.)  In Fig.\\ref{fig:const}, the overproduction of $^4$He due to the mass density of the gravitino at $T\\sim 1$MeV is also seen. The constraint from this effect is less stringent than those from the photo-dissociation of D and the present sneutrino mass density (discussed below).  If we assume that the sneutrino is the lightest SUSY particle, the sneutrinos produced by the gravitino decay are stable and their present mass density is given by \\begin{equation} \\Omega_{\\tilde{\\nu}}h^2 = 0.037 \\left(\\frac{m_{\\tilde{\\nu}}}{\\rm 100GeV}\\right) \\left(\\frac{T_R}{10^{10}\\GEV}\\right), \\label{density} \\end{equation} where $h$ is the Hubble constant in units of 100km/sec/Mpc.  Therefore the present limit on sneutrino mass 41GeV~\\cite{PD} sets the upperbound on the reheating temperature; \\begin{eqnarray} T_{R} \\leq 6.6\\times 10^{11}  h^{2}~\\GEV. \\label{ub-omega} \\end{eqnarray} This constraint is also shown in Fig.\\ref{fig:const}.\\footnote {In calculating eq.(\\ref{density}), we have ignored the effect of the pair annihilation of sneutrinos ($\\tilde{\\nu}+\\tilde{\\nu}^* \\rightarrow f + \\bar{f}$). For the pair annihilation process, the cross section is roughly estimated as $\\sigma v\\lesssim\\alpha_W/m_{\\tilde{\\nu}}^2$ (where $\\alpha_W$ is the coupling factor and $v$ is the relative velocity), and the condition for sufficiently large pair annihilation rate ($n_{\\tilde{\\nu}}\\sigma v \\gtrsim H$, with $n_{\\tilde{\\nu}}$ being the sneutrino density) reduces to $n_{\\tilde{\\nu}}/n_{\\gamma}\\gtrsim 10^{-7}$ (with $Y_{\\tilde{\\nu}}$ being the yield variable for the sneutrino), which is less stringent than the constraint (\\ref{ub-omega}). However, if the sneutrino mass is small enough to hit the pole of the $Z$-boson propagator, the constraint (\\ref{ub-omega}) becomes weaker, and constraint from the $^4$He overproduction may become significant for large gravitino mass ($\\mgra\\gtrsim 3\\TEV$).}  In summary, we have investigated the decay of the gravitino into a neutrino and a sneutrino, in particular, the effect on BBN by high energy photons induced by the decay. We have found the constraint on reheating temperature and mass of the gravitino as \\begin{equation} T_{R} \\lesssim 10^{10-12}\\GEV  ~~~~~~ {\\rm for} ~~~~ m_{3/2} =100\\GEV - 10\\TEV, \\end{equation} which is more stringent than the one obtained in ref.\\cite{PLB262-198}, but compatible with the rough estimation of the reheating temperature (\\ref{tr}) for a chaotic inflation.  \\subsection*{Acknowledgement}  We would like to thank T. Yanagida for useful discussions, and to K. Maruyama for informing us of the experimental data for photo-dissociation processes. One of the author (T.M.) thanks Institute for Cosmic Ray Research where part of this work has done.  This work is supported in part by the Japan Society for the Promotion of Science.  \\newpage  \\newcommand{\\Journal}[4]{{\\sl #1} {\\bf #2} {(#3)} {#4}} \\newcommand{\\APJ}{\\sl Ap. J.} \\newcommand{\\CJP}{\\sl Can. J. Phys.} \\newcommand{\\NC}{\\sl Nuovo Cimento} \\newcommand{\\NP}{\\sl Nucl. Phys.} \\newcommand{\\PL}{\\sl Phys. Lett.} \\newcommand{\\PR}{\\sl Phys. Rev.} \\newcommand{\\PRL}{\\sl Phys. Rev. Lett.} \\newcommand{\\PTP}{\\sl Prog. Theor. Phys.} \\newcommand{\\SJNP}{\\sl Sov. J. Nucl. Phys.} \\newcommand{\\ZP}{\\sl Z. Phys.}"
    }
}