9407.json

{
    "9407/astro-ph9407006_arXiv.txt": {
        "abstract": " ",
        "introduction": "Because of the extremely high temperatures that existed during the earliest moments it was too hot for nuclei to exist.  At around $1\\sec$ the temperature of the Universe cooled to $10^{10}\\,$K, and a sequence of events began that led to the synthesis of the light elements D, $^3$He, $^4$He and $^7$Li.  The successful predictions of big-bang nucleosynthesis provide the earliest and most stringent test of the big-bang model, and together with the expansion of the Universe and the $2.726\\,$K black-body cosmic background radiation (CBR) are the fundamental observational basis for the standard cosmology.  Big-bang nucleosynthesis began with the pioneering work of Gamow, Alpher, and Herman who believed that all the elements in the periodic table could be produced in the big bang \\cite{gamow}; however, it was soon realized that the lack of stable nuclei of mass 5 and 8 and Coulomb repulsion between highly charged nuclei prevent significant nucleosynthesis beyond $^7$Li.  In 1964, shortly before the discovery of the CBR, Hoyle and Tayler~\\cite{fredht} argued that the big bang must produce a large $^4$He abundance (about 25\\% by mass) and this could provide the explanation for the high \\He4 abundance observed in many primitive objects.  At about the same time, Zel'dovich realized that a lower temperature for the Universe today implied a greater mass fraction of \\He4 produced in the big-bang, and concluded that the big-bang model was in trouble. While his reasoning was correct, through a comedy of misunderstandings he mistakenly believed that the primeval mass fraction of $^4$He was at most 10\\% and that the temperature of the Universe was less than about $1\\,$K \\cite{zel}.  After the discovery of the CBR by Penzias and Wilson in 1965, detailed calculations of big-bang nucleosynthesis were carried out by Peebles~\\cite{pjep-bbn} and by Wagoner, Fowler and Hoyle~\\cite{wfh}.  It soon became clear that, as Hoyle and Tayler had speculated, the origin of the large primeval fraction of $^4$He was indeed the big-bang, and further, that other light elements were also produced. However, the prevailing wisdom was that \\D\\ and \\Li7 were produced primarily during the T~Tauri phase of stellar evolution and so were of no cosmological significance \\cite{fgh}. The amount of \\He4 produced in the big bang is very insensitive to the cosmic baryon---that is, ordinary matter---density (see Fig.~1), and thus it was not possible to reach any conclusions regarding the mean density of ordinary matter.  Since the other light elements are produced in much smaller quantities, ranging from $10^{-5}$ or so for D and $^3$He to $10^{-10}$ for $^7$Li (see Fig.~1), establishing their big-bang origin was a much more difficult task.  Further, it is complicated by the fact that the material we see today has been subjected to more than $10\\Gyr$ of astrophysical processing, the details of which are still not understood completely.  However, over the past 25 years the big-bang origin of D, $^3$He, and $^7$Li has been established, not only further testing the model, but also enabling an accurate determination of the average density of baryons in the Universe.  First, it was shown that there is no plausible astrophysical site for the production of deuterium~\\cite{rafs,els}; due to its fragility, post big-bang processes only destroy it.  Thus, the presently observed deuterium abundance serves as a {\\it lower limit\\/} to the big-bang production. This argument, together with the strong dependence of big-bang deuterium production on the baryon density, led to the realization that D is an excellent ``baryometer''~\\cite{rafs,ggst}, and early measurements of the deuterium abundance~\\cite{gr,ry}, a few parts in $10^5$ relative to hydrogen, established that baryons could not contribute more than about $20\\%$ of closure density.  This important conclusion still holds today.  The chemical evolution of $^3$He is more complicated. Helium-3 is produced in stars as they burn their primeval D before reaching the main sequence, and later by the nuclear reactions that cook hydrogen into helium.  Some massive stars destroy (or astrate) $^3$He.  It wasn't until the late 1970's that a suitable argument for $^3$He was found:   The present sum of D + $^3$He bounds their combined big-bang production \\cite{ytsso}.  Lithium was the last to come into the fold.  Stellar processes both destroy and produce $^7$Li; moreover, the abundance of $^7$Li varies greatly, from $^7$Li/H$\\,\\simeq 10^{-9}$ in the interstellar medium (ISM) to less than $^7$Li/H$\\,\\simeq 10^{-12}$ in some stars.  In 1982, Spite and Spite circumvented these difficulties by measuring the \\Li7 abundance in the oldest stars in our galaxy, metal-poor, pop II halo stars. They found $^7$Li/H$\\,\\simeq 10^{-10}$ \\cite{ss}, which is consistent with big-bang production. Their results established the case for the primeval \\Li7 abundance, which since has been strengthened by the work of others~\\cite{rmb-hp,thorburn}.  For the last decade much effort has been devoted to the critical comparison of the theoretical predictions and inferred primordial abundances of the light elements. The predictions depend upon the ratio of baryons to photons ($\\equiv \\eta$).  As we shall discuss in more detail, if $\\eta$ is between about $2.5\\times 10^{-10}$ and $6\\times 10^{-10}$ there is concordance between the predicted and measured abundances of all four light elements (see Fig.~1).  This leads to the best determination of the baryon density, \\begin{equation} \\rho_B = \\eta n_\\gamma m_N = 1.7\\times 10^{-31} \\gcmm3 \\hbox{--} 4.1 \\times 10^{-31}\\gcmm3 , \\end{equation} where the number density of photons, $n_\\gamma = 411 \\cmm3$, is known very precisely because the CBR temperature is so well determined~\\cite{firas}, $T_0 = 2.726\\,{\\rm K} \\pm 0.005\\,{\\rm K}$. On the other hand, because the critical density, \\begin{equation} \\rho_{\\rm crit} = 3H_0^2/8\\pi G = 1.88 h^2 \\times 10^{-29}\\gcmm3 , \\end{equation} depends upon the Hubble constant, which is still only known to within a factor of two, the fraction of critical density contributed by baryons is less well known: \\begin{equation} \\Omega_B = 0.009h^{-2} \\hbox{--} 0.02h^{-2} , \\end{equation} where $h\\equiv H_0/100\\kms\\Mpc^{-1}$. For a generous range for the Hubble constant, $h=0.4 - 1$, baryons contribute between 1\\% and 14\\% of closure density.  This fact has two profound implications.  First, since ``optically'' luminous matter (stars and associated material) contributes much less than 1\\% of the critical density, $\\Omega_{\\rm LUM} \\approx 0.003h^{-1}$ \\cite{omega-vis}, most baryons must be dark, e.g., in the form of hot, diffuse gas, or ``dark stars'' that have either exhausted their nuclear fuels (black holes, neutron stars or white dwarfs) or were not massive enough (less than about $0.08M_\\odot$) to ignite them.   In clusters of galaxies most of the baryonic matter seems to be in the form of hot, x-ray emitting gas.  Further, there is now indirect evidence for the existence of dark stars, known as MACHOs for Massive Astrophysical Compact Halo Objects, through their gravitational microlensing of distant stars \\cite{macho}.  Second, there is strong---though not yet conclusive---evidence that the average mass density of the Universe is significantly greater than 14\\% of the critical density \\cite{omega0}; if this is indeed the case, most of the mass density of the Universe must be ``nonbaryonic,'' with the most promising possibility being elementary particles left over from the earliest moments of the Universe \\cite{particledm}. Large-scale experiments are underway in laboratories all over the world to directly detect the nonbaryonic dark matter associated with the halo of our own galaxy \\cite{dmdetect}.  Big-bang nucleosynthesis plays the central role in defining both dark-matter problems which are central to cosmology today.  For example, the detection of temperature variations in the CBR by the COBE satellite was a dramatic confirmation of the general picture that structure evolved from small density inhomogeneities amplified by gravity.  One of the great challenges in cosmology is to formulate a coherent and detailed picture of the formation of structure (i.e., galaxies, clusters of galaxies, superclusters, voids, and so on) in the Universe; the nature of the dark matter is crucial to doing so.  Primordial nucleosynthesis also allows us to ``study'' conditions in the early Universe, and thereby, to probe fundamental physics in regimes that are beyond the reach of terrestrial laboratories.   For example, more than ten years ago the overproduction of $^4$He was used to rule out the existence of more than three light (mass less than about $1\\MeV$) neutrino species and constrain the existence of other light particle species \\cite{ytsso,nulimit,ossw,wssok}.  The remainder of this article is given to a careful assessment of the predictions and observations, paying special attention to the conclusions that can be sensibly draw about the baryon density. We begin with the easier part, a discussion of the theoretical predictions, where the few uncertainties are primarily statistical in nature and easy to quantify.  We then move on to the more difficult side, observations.  Here the situation is just the reverse:  The uncertainties are dominated by possible systematic errors and interpretational issues, which cannot be characterized by standard Gaussian error flags; care and judgment must be exercised to reach reliable conclusions. ",
        "conclusions": ""
    },
    "9407/gr-qc9407041_arXiv.txt": {
        "abstract": "The mechanism of the initial inflation of the universe is based on gravitationally coupled scalar fields $\\phi$. Various scenarios are distinguished by the choice of an {\\it effective self--interaction potential} $U(\\phi)$ which simulates a {\\it temporarily} non--vanishing {\\em cosmological term}. Using the Hubble expansion parameter $H$ as a new ``time\" coordinate, we can formally derive the {\\it general} Robertson--Walker metric for a {\\em spatially flat} cosmos. Our new method provides a classification of allowed inflationary potentials and is broad enough to embody all known {\\it exact} solutions involving one scalar field as special cases. Moreover, we present new inflationary and deflationary exact solutions and can easily predict the influence of the form of $U(\\phi)$ on density perturbations. ",
        "introduction": "The introduction of a {\\em cosmological constant} ${\\Lambda }$ in the field equations of general relativity later on stroke Einstein as ``the biggest blunder of my life'' \\cite{1,mtw}. Such an amendment was not even completely new, since von Seeliger \\cite{3} and Neumann \\cite{4}, e.g., have considered already in 1896 a corresponding term in the Poisson equation for the Newtonian potential in order to compensate the energy density of the `\\ae ther'.  Nowadays, Einstein's dream of a completely geometrical description of fundamental physical interactions has evolved into supergravity \\cite{5} and superstring models \\cite{6} in a way which was unprecedented at his times. Nevertheless, the cosmological term is still a major problem of these new approaches, as can be inferred from the review of Weinberg \\cite{7}.  The overall reason being that, in almost all quantized theories of particle interactions, the vacuum density $\\rho_{vac}$ gives rise to a huge {\\em bare} cosmological constant $\\Lambda_0 = \\kappa \\rho_{vac}$. This can be traced back to the fact that the vacuum fluctuations feel all the complicated physics originating from Higgs fields, fermion condensates etc., which enter into today's unified field theories. For much higher energies or, equivalently, to very short spacetime distances, the small scale behavior of the quantum world would determine the large scale structure of the universe.  On the other hand, it is known that the observed macroscopical energy density ${\\epsilon}$ is extremely small. For the range of 45--100 km s$^{-1}$ Mpc$^{-1}$ of {\\em today's} Hubble constant $H_0$, the critical density is estimated as $\\rho_c = 0.5 - 2 \\times 10^{-29}$ g/cm$^3$. From local as well as large scale astronomical measurements, respectively, the macroscopically observed cosmological constant ${\\Lambda}$ is estimated \\cite{8} to be less than $4\\times 10^{-56}$ cm$^{-2}$. Since the vacuum energy may also be time--dependent at the early stages of the universe, the exact fine--tuning of the various vacuum contributions to a very small ${\\Lambda}$ in the low temperature regime of today appears to be one of the great mysteries about unification.  Higgs--type scalar fields become more and more important. They are not only induce the masses for the elementary particles via the Higgs--Kibble mechanism, but they can also form stable boson stars \\cite{kusm} and kinks \\cite{baek}. For spin--one--particles, exact non--singular solutions of the Einstein--$SU(2)$--Yang--Mills system are not yet known, but the new power series expansion technique of Ref.~\\cite{sch2} can be regarded as a first attemption in this direction.  But the scalar fields, in disguise as the ``inflaton'' $\\phi $, can also dominate the early universe, the {\\em epoch of inflation}. Before symmetry breaking, a self--interaction $U(\\phi )$ of such gravitationally coupled scalar fields allows us to introduce a {\\em variable} ``cosmological term\" without violating the Noether--Bianchi identities of Einstein's general relativity.   \\section {\\bf Model of a universe with inflation}   $\\!$ From new astronomical observations (COBE) we know that the universe expands, is rather homogenious on the large scale and in the microwave background. However, the standard Friedmann model of the cosmos offers no solution to such issues as the singularity problem, the problem of flat space, the horizont problem, the homogenity problem on great scales, the absence of magnetic monopoles \\cite{mie86}, and the problem of large number of particles \\cite{linde,brandenberger}.  The idea of {\\em inflation} (see Guth \\cite{guth} and Linde \\cite{linde82}) attempts to solve several of these problems. Scalar fields (Higgs, axion) are expected to generate, shortly after the big bang, an exponential increase of the universe. However, in these first attempts, there was no so--called {\\em graceful exit} to the Friedmann cosmos, and the inflationary phase did not end. This problem was solved in the {\\em new inflationary universe}. In this model, the scalar field is ruled by a slightly different self--interaction potential which possesses a slow--roll part (a plateau) of the potential (acting as a vacuum energy) which dominates the universe at the beginning.  Later on, power--law models were constructed which possess no exponential but an $a(t) \\sim t^n$ increase of the expansion factor of the universe \\cite{lucmat,barrow87}. The {\\em intermediate inflation} is merely a combination of exponential and power--law increase \\cite{barrow90}. Mathematically, inflation is described by a positive second derivative of the scale factor $a(t)$ of the universe. In general, this requires $\\rho + 3p < 0$, where $\\rho $ is the density and $p$ the pressure of the matter field.  In the models of the new and chaotic inflationary models, we have a fine--tuning problem which consists of the combination of the largeness of the scale factor and an acceptable distribution for density perturbations \\cite{stein}. Solutions for these problems are attempted in the scenarios of {\\em extended inflation} \\cite{stein,laste,barmae}.  In all of these models, the isotropy and homogenity are prescribed. It was also shown that all initially expanding homogeneous models (the Bianchi and Sachs--Kantowski universes) which include a positive cosmological constant, approach asymptotically the de Sitter solution \\cite{wald,turner} which is isotropic. This is called the ``cosmic no--hair'' theorem. For models with scalar inflation, the question of damping a possibly initial anisotropy of the universe is not relevant, because the model merely has to a ensure a very small anisotropy in the universe after inflation \\cite{barrow93}.   In this paper, we present in Sec.~5 a general inflationary solution in terms of the Hubble parameter which comprise all previous exact solutions. This enables us, in Sec.~6, to classify the potential $U(\\phi )$ for the scalar field according to the different onset of inflationary, deflationary, and Friedmann phases of the universe. Within this new description, some new exact solutions of the so--called {\\em new} and {\\em chaotic} type are found in Sec.~8, 9, and 10. The potentials found have a rather complicated form which, however, have so far no motivation from field theory.  Recently {\\it chaotic models} with {\\em several} scalar fields $\\phi_I$ including the inflaton have attracted much attention. Linde termed his model ``hybrid inflation\" \\cite{lin94}, cf. Copeland et al.~\\cite{cope94}. In the vacuum dominated regime, the back reaction of the other scalar field on the inflaton is negligible and we can follow their evolution explicitly by using quantum field theory in curved spacetime, in the case of a de Sitter background, see \\cite{mie77}, for example. In these hybrid models, all the other scalar fields vanish, if they sit in the false vaccum. For the remaining inflaton, we can then simply apply the general solution of Sect.~\\ref{7}.   \\section {\\bf Friedmann spacetime}   For a rather general class of inflationary models the Lagrange density reads \\be {\\cal L} = \\frac{1}{2 \\kappa } \\sqrt{\\mid g \\mid} \\Biggl ( R + \\kappa \\Bigl [ g^{\\mu \\nu } (\\partial_\\mu \\phi ) (\\partial_\\nu \\phi ) - 2 U(\\phi ) \\Bigr ] \\Biggr )  \\; , \\label{lad} \\ee where $\\phi $ is the scalar field and $U(\\phi )$ the self--interaction potential. We use natural units with $c=\\hbar =1$. A constant potential $U_0= \\Lambda / \\kappa $ would simulate the cosmological constant $\\Lambda $. Scalar coupled Jordan--Brans--Dicke type \\cite{brans} models can be reduced to (\\ref{lad}) via the Wagoner--Bekenstein--Starobinsky transformation \\cite{wag,beken,kasp,galt}. We are looking for solutions of the Einstein equation \\be R_{\\mu \\nu } - \\frac {1}{2} g_{\\mu \\nu } R = - \\kappa T_{\\mu \\nu } \\; , \\ee which are of the Robertson--Walker type \\ben ds^2 & = & dt^2 - a^2(t) \\left [ \\frac{dr^2}{1 - k r^2} + r^2 \\left ( d\\theta^2 + \\sin^2 \\theta d \\varphi^2 \\right ) \\right ] \\; , \\nonumber \\\\ & & \\qquad k = 0, \\pm 1 \\; , \\label{rw} \\een where $a(t)$ is the expansion factor with the dimension {\\em length}. An open, flat, or closed universe is characterized by $k=-1,0,1$, respectively. This means that we will investigate {\\em homogeneous and isotropic} spacetimes. The scalar field depends only on the time $t$, i.e.~$\\phi = \\phi(t)$. Then, the only non--vanishing components of the energy--momentum tensor read \\ben \\rho & = & T_0{}^0 = \\frac {1}{2} \\dot \\phi^2 + U  \\; , \\\\ p & = & - T_1{}^1 = - T_2{}^2 = - T_3{}^3 = \\frac {1}{2} \\dot \\phi^2 - U \\; . \\een   \\section {\\bf Reparametrized self--interaction}   Let us assume that $a(t) \\neq 0$, furthermore, we express our result in terms of the Hubble expansion rate \\be H := \\frac {\\dot a(t)}{a(t)} \\; .  \\label {H(t)} \\ee Only the diagonal components of the Einstein equation are non--vanishing. The $(0,0)$ component is \\be 3 \\left ( H^2 + \\frac {k}{a^2} \\right ) = \\kappa \\rho   \\; . \\label{1} \\ee It describes the conservation of the energy. The $(1,1)$, $(2,2)$, and $(3,3)$ components are given by \\be 2 \\dot H + 3 H^2 + \\frac {k}{a^2} = - \\kappa p  \\; . \\label{2} \\ee The resulting Klein--Gordon equation is \\be \\ddot \\phi = - 3 H \\dot \\phi - U'(\\phi ) \\; , \\label{scalar} \\ee which, after multiplication by $\\dot \\phi $, can be transformed into \\be \\frac {1}{2} ((\\dot \\phi)^2) \\dot{} = - 3 H (\\dot \\phi )^2 - \\dot U \\; . \\label{scatra} \\ee From (\\ref{1}) and (\\ref{2}) we obtain by linear combination \\be \\dot H = \\frac {k}{a^2} - \\frac {\\kappa }{2} (\\rho + p) = \\frac {k}{a^2} - \\frac {\\kappa }{2} \\dot \\phi^2  \\label {2'} \\ee and \\ben \\dot H + 3 H^2 + \\frac {2k}{a^2} & = & \\frac {\\kappa }{2} (\\rho - p) \\label {min}\\\\ & = & \\kappa U  \\; . \\nonumber \\een Observe that (\\ref{min}) is, in view of (\\ref{scatra}) and (\\ref{2'}), a {\\it first integral} of (\\ref{scalar}) for all values of the normalized extrinsic curvature scalar $k$. Alternatively, if we eliminate the $k/a^2$ terms in equations (\\ref{1}) and (\\ref{2}), we obtain the Raychaudhuri equation \\be \\dot H + H^2 = \\frac {\\ddot a}{a} = - \\frac {\\kappa }{6} (\\rho + 3p) \\; . \\label {ray} \\ee  There are several options to calculate solutions for the given system of differential equations (\\ref{1}) and (\\ref{2}) or (\\ref{2'}) and (\\ref{min}), respectively. The first possibility is to assume a reasonable functional dependence of the scale factor $a(t)$ and then to calculate simply the Hubble expansion rate $H(t)$. However, even for $k=0$ the equation (\\ref{2'}) is not easily integrable in closed form.  Secondly, one could imagine a potential $U(\\phi )$ which possesses the physically desirable features, and consider (\\ref{2'}) and (\\ref{min}), which, for $k=0$, form the autonomous nonlinear system \\ben \\dot H & = & \\kappa U(\\phi ) - 3H^2 \\; , \\label{doth} \\\\ \\dot \\phi & = & \\pm \\sqrt {\\frac {2}{\\kappa }} \\sqrt{3H^2 - \\kappa U(\\phi )} \\; .\\label{dotphi} \\een In the phase space \\cite{piran}, the equilibrium states of this system are given by the constraint $\\{ \\dot H,\\dot \\phi \\}=0$. This constraint is fulfilled by $\\kappa U(\\phi ) = 3H^2$, where the Hubble expansion rate is constant, i.e.~$H_0=\\sqrt{\\Lambda /3 \\,}$. For $\\dot \\phi=0$, we obtain a de Sitter--type inflation with $a(t)=\\exp (\\sqrt{\\Lambda /3 \\, } t)$.  For $\\kappa U(\\phi ) \\neq 3H^2$, we find $\\{ \\dot H, \\dot \\phi \\} \\neq 0$, which implies that the solution $\\phi = \\phi (t)$ and $H=H(t)$ are {\\em invertible}. Then we can write the potential in (\\ref{doth}) and (\\ref{dotphi}) in the {\\em reparametrized} form \\be U(\\phi ) = U(\\phi (t)) = U(\\phi (t(H))) = \\widetilde U(H)  \\; . \\label{uh} \\ee Another question is whether it is possible to construct $H=H(t)$ from the {\\em inverse} function $t=t(H)$ in closed form. Only in this case, the Hubble expansion parameter and the scalar field can be expressed explicitly as a function of time, and the self--interaction potential $U(\\phi )$ can be recovered from $\\widetilde U(H)$.   \\section {\\bf General metric of a spatially flat inflationary universe \\label{7}}   In view of (\\ref{1}), (\\ref{2}), and (\\ref{uh}), for $k=0$, the density and the pressure can be reexpressed as \\ben \\rho & = & \\frac {3}{\\kappa } H^2 \\label{dens} \\; , \\\\ p & = & - \\rho - \\frac {2 \\dot H}{\\kappa } \\\\ & = & \\rho - 2 \\widetilde U  \\label{rho-2u} \\; . \\een Hence, the density $\\rho $ is always a positive function, whereas the pressure $p$ is indefinite and changes sign at $\\kappa \\widetilde U = 3H^2/2$.  For $\\kappa \\widetilde U \\neq 3H^2$, we find from (\\ref{doth}) and (\\ref{uh}) the formal solution for the coordinate time \\be t = t(H) = \\int \\frac {dH}{\\kappa \\widetilde U - 3 H^2}  \\label{tH} \\; . \\ee In formal expressions involving indefinite integrals, we omit the constant of integration. The scale factor in the metric follows from the definition (\\ref{H(t)}) of the Hubble expansion rate as $a(t)=a_0 \\exp (\\int H dt)$ where $a_0$ is a constant with dimension {\\em length}. Inserting (\\ref{tH}), we thus can determine the general solution as \\be a = a(H) = a_0 \\exp \\left ( \\int \\frac {H dH}{\\kappa \\widetilde U - 3 H^2} \\right )  \\label{aH} \\; . \\ee  This implies for $k=0$ that the reparametrized Robertson--Walker metric for inflation reads \\ben ds^2 & = & \\frac {dH^2}{\\left (\\kappa \\widetilde U - 3 H^2 \\right )^2} - a_0{}^2 \\exp \\left ( 2 \\int \\frac {H dH}{\\kappa \\widetilde U - 3 H^2} \\right ) \\times  \\nonumber \\\\ & &   \\left [ d r^2 + r^2 \\left ( d \\theta^2 + \\sin^2 \\theta d \\varphi^2 \\right ) \\right ] \\; . \\een Note that the Hubble expansion rate $H$ has become the (inverse) time coordinate. This resembles the reparametrization of Hughston, cf.~\\cite[p.~731]{mtw}, for the Friedmann solution, in which $a(t)$ serves as the new time parameter. In view of (\\ref{tH}), the general solution of (\\ref{dotphi}) for the scalar field can be calculated in terms of the Hubble parameter $H$ as \\be \\phi = \\phi (H) = \\mp \\sqrt {\\frac{2}{\\kappa }} \\int \\frac {dH}{\\sqrt{3H^2-\\kappa \\widetilde U}} \\; . \\label{phiH} \\ee Our general formula (\\ref{phiH}) resembles the Wagoner--Starobinsky transformation from the conformal Brans--Dicke frame to an Einstein frame, cf.~\\cite{kasp}. In metric--affine gauge theories of gravity \\cite{hehl} this transformation has a rather natural origin from generalized conformal changes of the metric.  If we introduce the conformal time $T$ via $dt=a(t)\\, dT$, the Robertson--Walker metric (\\ref{rw}) (for $k=0$) acquires the manifest conformally flat form \\be ds^2= a^{2}(t) \\left [ dT^2 - dr^2 - r^2 \\left ( d\\theta^2 + \\sin^2 \\theta d \\varphi^2 \\right ) \\right ] \\; . \\ee For our general solution, the conformal time can be expressed by the relation \\be dT= {{dH}\\over{\\kappa \\widetilde U -3H^2}}\\, \\exp\\int {{HdH}\\over{3H^2-\\kappa \\widetilde U}} \\; . \\ee  Our general solution holds for $k=0$ and for $\\widetilde U \\neq 3H^2/\\kappa $. Since this singular case leads to the de Sitter inflation, we try in the explicit models the ansatz \\be \\widetilde U(H) = \\frac {3}{\\kappa } H^2 + \\frac {g(H)}{\\kappa} \\ee for the potential, where $g(H)$ is a nonzero function for the {\\em graceful exit}.   \\section {\\bf Allowed inflationary potentials}  Inflation and deflation necessarily occur for all potentials which satisfy the matter condition $\\rho + 3p<0$, i.e.~$\\ddot a(t)>0$. In order to discriminate inflationary from deflationary models, one has to take into account also the rate of change of the scale factor $a(t)$ or the sign of the Hubble expansion rate, respectively. For {\\em inflation}, we require \\be \\ddot a > 0 \\; , \\quad \\dot a > 0 \\quad \\Longleftrightarrow \\quad  H>0 \\; , \\ee whereas for {\\em deflation} we require \\be \\ddot a > 0 \\; , \\quad \\dot a < 0 \\quad \\Longleftrightarrow \\quad  H<0 \\; . \\ee  For a classification of the potentials, we follow Ref.~\\cite[p.~773]{mtw} and call \\ben q(t) & := & - \\frac {\\ddot a a}{\\dot a^2} = - \\left (1 + \\frac {\\dot H}{H^2} \\right ) \\\\ & = & 2 - \\kappa \\frac {\\widetilde U}{H^2} \\een the {\\it deceleration parameter}. Because $\\dot a^2$ and $a$ are positive, an accelerating cosmos $(\\ddot a >0)$ is described by negative $q$ values. Thus, acceleration can only occur for a potential satisfying \\be \\kappa \\widetilde U > 2 H^2 \\; . \\ee  According to (\\ref{rho-2u}) the pressure is then necessarily negative and {\\em drives} the inflation. Another constraint is found by looking at the general solution for the scalar field (\\ref{phiH}). The scalar field remains real only if the potential fulfills $\\kappa \\widetilde U < 3 H^2$. [Otherwise, we would have a scalar ``ghost\" in the Lagrangian (\\ref{lad}).] From Fig.~\\ref{fig.0}, we can read off the different regions of the potential. All values within the parabola, i.e.~$\\kappa \\widetilde U > 3 H^2$, are forbidden. All points on the curve $\\widetilde U=3 H^2$ are singular for our system (\\ref{doth}) and (\\ref{dotphi}) and describe the de Sitter solution. The origin is the flat and empty Minkowski spacetime. Solutions within the domain \\be 2H^2< \\kappa \\widetilde U<3H^2 \\quad {\\mbox{and}} \\quad H>0 \\label{infl} \\; , \\ee bounded by parabolas, describe universes with {\\em inflation}. Solutions within the domain \\be 2H^2< \\kappa \\widetilde U<3H^2 \\quad {\\mbox{and}} \\quad  H<0 \\label{defl} \\ee describe universes with {\\em deflation}. If these solutions leave this area through $\\kappa \\widetilde U=2H^2$, they make contact with a Friedmann cosmos for which $\\ddot a <0$.  According to \\cite{mie77}, the discrimination between inflation and deflation depends on the choice of the conformal frame. For the scalar matter, we find from (\\ref{ray}) that $\\rho + 3p=2 (\\dot \\phi^2 - \\widetilde U)$. For potential--dominated eras this term is negative and hence inflation can occur. The condition for inflation $\\ddot a >0$ is then equivalently to $\\dot H > -H^2$.  For $k=0$ and scalar matter, we can infer from (\\ref{2'}) that always $\\dot H<0$, i.e.~$-H^2<\\dot H < 0$. For other types of matter it is possible that $\\dot H>0$, cf.~eg.~the spin driven inflation \\cite{obuk}. Such physical models are also called {\\em superinflationary}, in contrast to the {\\em subinflationary} ones \\cite{kolb,lid,lucmat} considered here.  Several models are now conceivable which have combinations of in- and deflationary potentials. One can construct models where inflation never ends, those with a combined inflation--Friedmann cosmos, or some where the universe enters the deflationary regime. In the following, we will recover known models from our general formalism and present some new ones, too.   \\section {\\bf Power--law and intermediate inflation}   The ansatz \\be g(H) = - A \\, H^{n} \\; , \\ee where $n$ is real and $A$ a positive constant, leads to several known and new solutions. The integration constants $C_1,C_2,C_3$ are, of course, different in every model. As it turns out, $n=0,1,2$ are special cases which we consider first:  For $n=0$, we find the following solution: \\be H(t)=- (A t + C_1)  \\; , \\quad a(t) = a_0 \\exp \\left ( -\\frac{1}{2A} (A t+C_1)^2 + C_2 \\right ) \\; , \\ee and \\be \\phi (t) = \\pm \\sqrt{ \\frac {2A}{\\kappa } } (At+C_1-C_3)  \\; . \\ee The chronology in this model is the following: at first, there is an inflationary phase for which the maximal size of the universe is $a_0 \\exp (-C_1/(2A)+C_2)$. This is very extended for $C_1<<0$ or $C_2>>0$. The transition from inflation to the standard Friedmann cosmos occurs at the point $H=+\\sqrt{A}$. There exists also a transition from the standard Friedmann cosmos to deflation which occurs at $H=-\\sqrt{A}$. This all can also be recognized by looking at the classification diagram (Fig.~\\ref{fig.0}). The self--interaction potential is only {\\em quadratic} as it is normally investigated in the chaotic scenario: \\be U(\\phi ) = \\frac {1}{\\kappa } \\left [ 3 \\left ( \\sqrt { \\frac {\\kappa }{2A}} \\phi + C_3 \\right )^2 - A \\right ] \\; . \\ee  For $n=1$ we have \\be H(t)= C_1 \\exp (-A t) \\; , \\quad a(t) = a_0 \\exp \\left (- \\frac{C_1}{A} \\exp (-At) + \\frac {C_2}{A} \\right ) \\; , \\ee and \\be \\phi (t) = \\pm \\sqrt{ \\frac {8}{A \\kappa } } \\left [ \\sqrt{C_1} \\exp \\left ( \\frac {-At}{2} - C_3 \\right ) \\right ] \\; , \\ee so that $C_1>0$. The universe in this model starts with an inflationary phase up to the point $H=A$, where it crosses the boundary $\\kappa \\widetilde U = 2H^2$ and evolves towards a conventional Friedmann cosmos. The universe reaches the size $a_0 \\exp (C_2/A)$ after infinitely long time. The potential \\be U(\\phi ) = \\frac {A}{8} e^{2 C_3} \\phi^2 \\left ( \\frac {3 \\kappa A}{8} e^{2 C_3} \\phi^2 - A \\right ) \\ee has here a linear combination of $\\phi^2$-- and $\\phi^4$--terms which are familiar from the Higgs potential of spontaneous symmetry breaking. For a pure $\\phi^4$--potential, an exact and an approximate solution is found in Refs.~\\cite{gott} and \\cite{lin83}.  For $n=2$ we find \\be H(t)=\\frac {1}{At+C_1}  \\; , \\quad  a(t) = a_0 (C_2 (At+C_1))^{1/A}  \\; , \\ee and \\be \\phi (t) = \\pm \\sqrt{\\frac{2}{A\\kappa }} \\ln \\left ( \\frac {1}{C_3 (At+C_1)} \\right ) \\; . \\ee The self--interaction is the exponential potential \\be U(\\phi ) = \\frac {3-A}{\\kappa } C_3{}^2 \\exp (\\pm \\sqrt{2 \\kappa A}\\; \\phi ) \\; . \\ee This case describes power--law inflation $t^{1/A}$ if $0<A<1$, which means that $2H^2< \\kappa U<3H^2$ and $H>0$. For $A=3/2$ the pressure (\\ref{rho-2u}) of the scalar field vanishes and we get $a(t) \\simeq t^{2/3}$ as in the matter--dominated Friedmann cosmos \\cite{steph}. One recognizes that for $A=3$ the scalar field possesses a vanishing potential (see the Appendix).  For $n\\neq 0,1,2$ the constant $A$ has the dimension $length^{n-2}$. For the Hubble expansion rate, we get \\be H = \\left ( A (n-1) (t+C_1) \\right )^{1/(1-n)} \\; , \\ee whereas the scale factor reads \\be a(t) = a_0 \\exp \\left [ (A (n-1))^{1/(1-n)} \\frac {1-n}{2-n} (t+C_1)^{(2-n)/(1-n)} \\right ] \\; . \\ee The scalar field is then given by \\be \\phi (t) + C_3 = \\sqrt { \\frac {2}{A \\kappa } } \\frac {2}{2-n} \\Bigl [ A (n-1) (t+C_1) \\Bigr ]^{(2-n)/(2(1-n))}  \\; . \\ee The corresponding potential reads \\ben U(\\phi ) & = & \\frac {1}{\\kappa } \\left [ \\sqrt{\\frac {\\kappa A}{8}} (2-n) \\left ( \\phi + C_3 \\right )^{2/(2-n)} \\right ] \\times \\nonumber \\\\ & &  \\left ( 3 \\frac {\\kappa A}{8} (2-n)^2 \\left ( \\phi + C_3 \\right )^2 - A \\left (\\frac {\\kappa A}{8} \\right )^{n/2} (2-n)^n \\left ( \\phi + C_3 \\right )^n \\right )  \\; . \\label{un} \\een Hence, we recover the models \\cite{barrow90} of intermediate inflation $\\exp (t^{(2-n)/(1-n)})$ with $0<(2-n)/(1-n)<1$, which is equivalent to $1<n<2$. For $(2-n)/(1-n)=2/3$, the flat Harrison--Zel'dovich spectrum is recovered. Translated into our model this holds for $n=4$, i.e. \\be \\kappa \\widetilde U = 3H^2 - AH^4 \\; . \\label{n=4} \\ee   \\section {\\bf New potential in the framework of chaotic inflation}   Another model can be obtained from the ansatz \\be g(H) = \\pm \\frac {4}{C} \\sqrt{A C H - H^2}\\, H \\; , \\ee where $A,C$ are constants. For this model we find the scale factor \\be a(t) = a_0 \\exp [C \\arctan (At+B)+F] \\; , \\ee see Fig.~\\ref{fig.1.1}. For \\be a(t) = a_0 \\exp [C \\mbox{arccot} (-A t)+F] \\; , \\ee we find the same model, but the scale factor reaches for $t \\rightarrow \\infty $ another limit $(A>0)$: $ a_0 \\exp ( C \\pi )$.  The Hubble expansion rate is \\be H(t) = \\frac {A C}{1+(At+B)^2} \\; , \\ee which vanishes for $t \\rightarrow \\infty $. The solution of the scalar field (Fig.~\\ref{fig.1.2}) was determined via the computer algebra system {\\em Macsyma} as \\ben \\phi (t) & = & \\pm \\sqrt{ \\frac {2C}{\\kappa }} \\Biggl \\{ \\biggl [ \\arctan \\Bigl ( \\sqrt{2(At+B)} +1 \\Bigr ) \\nonumber \\\\ & & + \\arctan \\Bigl (\\sqrt{2(At+B)} -1 \\Bigr ) \\biggr ] \\nonumber \\\\ & & - \\frac {1}{2} \\biggl [ \\ln \\Bigl (At+B+\\sqrt{2(At+B)}+1 \\Bigr ) \\nonumber \\\\ & & - \\ln \\Bigl (At+B-\\sqrt{2(At+B)}+1 \\Bigr ) \\biggr ] \\Biggr \\} + C_1  \\; . \\label{phi1} \\een  In the following, we will only consider this model with positive scalar field. The potential $U$ depending on the time $t$ reads \\be U(t) = \\frac {A^2 C}{\\kappa } \\frac {3C - 2At - 2B}{[1+(At+B)^2]^2} \\; . \\ee Because of the complicated functional dependence of $\\phi (t)$, we have not found a closed form of the inverse function, but have numerically determined $U(\\phi )$, see Fig.~\\ref{fig.1.3}. This potential has {\\em no} plateau at the origin $\\phi =0$. But it possesses a minimum with a negative value of $U$. After the minimum a limiting point follows, for which the potential vanishes: The scalar field needs infinitely long in order to reach this point.  Eq.~(\\ref{phi1}) gives the constraints $C>0$ and $At+B>0$ on the integration constants. Real solutions occur only for initial times $t_i \\ge -B/A$. The condition \\cite{barlid} for an inflationary phase is in general given by (\\ref{infl}). For $A>0$ we have $\\dot a >0$ and find \\be \\ddot a (t) = \\frac {A^2 C \\exp [C \\arctan (At+B)]}{(1+B^2+2ABt+A^2t^2)^2} \\Bigl ( C - 2 A t - 2 B ) \\Bigr ) \\; . \\ee In each model, depending on the constants $A,B,C$, the scale factor starts with the value $a(-B/A)=1$, the velocity $\\dot a(-B/A)=A C$, and the acceleration $\\ddot a(-B/A)=A^2 C^2$. Then the universe inflates exponentially up to the time $t_f=(C-2B)/(2A)$ $\\Leftrightarrow \\; \\ddot a =0$ ($f$ means final). Then, a positive pressure of the scalar field prevents a further expansion of the universe. Hence, the duration of inflation is $t_f - t_i = C/(2A)$. Only the constant $C$ determines the strength of inflation whereas both constants $A$ and $C$ determine the duration of the inflation. The constant $B$ has no geometrical meaning. At the end of inflation the scale factor is constant. After infinitely long time, in practice, very soon after the inflation phase, a Minkowski spacetime emerges.  It is also possible to take into account a de Sitter type expansion, i.e.~the Hubble expansion rate is becoming constant after a short starting phase determined by the new model. We may connect the two models by \\be a(t) = a_0 \\exp [C \\arctan (A t + B) + D t + E]  \\; . \\ee Then, we find \\be H = \\frac {A C}{1+(At+B)^2} + D  \\longrightarrow  D \\; . \\ee We get the same solution for the scalar field, whereas the time--dependent potential is changed to \\ben U(t) & = & \\frac {3}{\\kappa } \\left ( \\frac {A C}{1+(At+B)^2} + D \\right )^2 \\nonumber \\\\ & & - \\frac {2 A^2}{\\kappa } \\frac {(At + B) C}{(1+(At+B)^2)^2} \\; , \\een so that in the limit $t \\rightarrow \\infty $ we have: $U \\rightarrow 3D^2/\\kappa $. The disadvantage of this model is that the de Sitter inflation very soon plays the decisive role and inflation never ends. ",
        "conclusions": ""
    },
    "9407/astro-ph9407027_arXiv.txt": {
        "abstract": "The topic of this letter is structure formation with topological defects. We first present a partially new, fully local and gauge invariant system of perturbation equations to treat microwave background and dark matter fluctuations induced by topological defects (or any other type of seeds). We show that this treatment is  extremly well suited for  linear numerical analysis  of structure formation by applying it to the texture scenario. Our numerical results cover a larger dynamical range than previous investigations and are complementary since we use substantially different methods. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9407/astro-ph9407056_arXiv.txt": {
        "abstract": "Some of the technical details involved in taking and analyzing data from the \\COBE\\ are discussed, and recent results from the FIRAS and DMR experiments are summarized. Some of the cosmological implications of these recent data are presented. ",
        "introduction": "The \\COBE\\ mission is the product of many years of work by a large team of scientists and engineers.  Credit for all of the results presented in these lectures must be shared with the other members of the the \\COBE\\ Science Working Group: Chuck Bennett, Ed Cheng, Eli Dwek, Mike Hauser, Tom Kelsall, John Mather, Harvey Moseley, Nancy Boggess, Rick Shafer, Bob Silverberg, George Smoot, Steve Meyer, Rai Weiss, Sam Gulkis, Mike Janssen, Dave Wilkinson, Phil Lubin, and Tom Murdock. Bennett \\etal\\ (1992a) is an excellent review of the history of the \\COBE\\ project and its results up to the discovery of the anisotropy by the DMR, but not including the latest FIRAS limits on distortions.  Some of the members of this team have been working on \\COBE\\ since 1974, when the proposals for what became the \\COBE\\ project were submitted.  I have been working on \\COBE\\ since the beginning of 1978. \\COBE\\ was successfully launched on 18 November 1989 from California, and returned high quality scientific data from all three instruments for ten months until the liquid helium ran out.  But about 50\\% of the instruments do not require liquid helium, and are still returning excellent scientific data in January 1993. While the \\COBE\\ mission has been very successful, making the ``discovery of the century'', one must remember that this work is based on the earlier work (in the $20^{th}$ century!) of Hubble (1929) and Penzias and Wilson (1965), who discovered the expansion of the Universe and the microwave background itself.  As a consequence of these two discoveries, one knows that the early Universe was very hot and dense. When the density and temperature are high, the photon creation and destruction rates are very high, and are sufficient to guarantee the formation of a very good blackbody spectrum.  Later, as the Universe expands and cools, the photon creation and destruction rates become much slower than the expansion rate of the Universe, which allow distortions of the spectrum to survive.  In the standard model the time from which distortions could survive is 1 year after the Big Bang at a redshift $z \\approx 10^{6.4}$.  However, the action of the expansion itself on a blackbody results in another blackbody with a lower temperature.  Thus the existence of a distorted spectrum in the hot Big Bang model requires the existence at time later than 1 year after the Big Bang of both an energy source and an emission mechanism that can produce photons that are now in the millimeter spectral range.  Conversely, a lack of distortions can be used to place limits on any such energy source, such as decaying neutrinos, dissipation of turbulence, etc.  At a time $3\\times10^5$ years after the Big Bang, at $z \\approx 10^3$, the temperature has fallen to the point where helium and then hydrogen (re)combine into transparent gases. The electron scattering which had impeded the free motion of the CMB photons until this epoch is removed, and the photons stream across the Universe.  Before recombination, the radiation field at any point was constrained to be very nearly isotropic because the rapid scattering scrambled the directions of photons. The radiation field was not required to be homogeneous, because the photons remained approximately fixed in comoving co-ordinates.  After recombination, the free streaming of the photons has the effect of averaging the intensity of the microwave background over a region with a size equal to the horizon size.  Thus after recombination any inhomogeneity in the microwave background spectrum is smoothed out. Note that this inhomogeneity is not lost: instead, it is converted into anisotropy. When we study the isotropy of the microwave background, we are looking back to the surface of last scattering 300,000 years after the Big Bang. But the hot spots and cold spots we are studying existed as inhomogeneities in the Universe before recombination. Since the $7^\\circ$ beam used by the DMR instrument on \\COBE\\ is larger than the horizon size at recombination, these inhomogeneities cannot be constructed in a causal fashion during the epoch before recombination in the standard Big Bang model.   Instead, they must be installed ``just so'' in the initial conditions.  In the inflationary scenario of Guth (1980), these large scale structures were once smaller than the horizon size during the inflationary epoch, but grew to be much larger than the horizon.  Causal physics acting $10^{-35}$~seconds after the Big Bang can produce the large-scale inhomogeneities studied by the DMR. ",
        "conclusions": "So far \\COBE\\ has been a remarkably successful space experiment with dramatic observational consequences for cosmology.  The third instrument on \\COBE\\ is the DIRBE instrument, which I have not had time to talk about. The DIRBE is searching for a cosmic infrared background, and faces the difficulty that the CIB is expected to be many times fainter than the local infrared backgrounds from the Solar System and the Milky Way."
    },
    "9407/gr-qc9407023_arXiv.txt": {
        "abstract": "We modify the recent analytic formula given by Allen and Casper \\cite{AllenCasper} for the rate at which piecewise linear cosmic string loops lose energy to gravitational radiation to yield the analogous analytic formula for the rate at which loops radiate momentum.  The resulting formula (which is exact when the effects of gravitational back-reaction are neglected) is a sum of $O(N^4)$ polynomial and log terms where, $N$ is the total number of segments on the piecewise linear string loop. As illustration, we write the formula explicitly for a simple one-parameter family of loops with $N=5$.  For most loops the large number of terms makes evaluation ``by hand\" impractical, but, a computer or symbolic manipulator may by used to yield accurate results.  The formula has been used to correct numerical results given in the existing literature.  To assist future work in this area, a small catalog of results for a number of simple string loops is provided. ",
        "introduction": "\\label{section1} Cosmic strings are one-dimensional topological defects that may have formed at phase transitions as the universe expanded and cooled \\cite{Kibble,Zel'dovich,Vilenkin,SV}.  A cosmic string loop is formed when two sections of long string (a string with length greater than the horizon length) meet and intercommute.  After a loop is formed, it begins to oscillate under its own tension.  As cosmic string loops oscillate, they lose energy in the form of gravitational radiation. The formation and subsequent decay of cosmic string loops is of fundamental importance to the evolution of the cosmic string network. In addition, most of the observational limits on cosmic strings are obtained by considering the effects of the gravitational radiation emitted as the loops decay ($\\!$\\cite{SV,AllenCaldwell} and references therein).  The power emitted in gravitational radiation by a cosmic string loop depends upon its shape and velocity.  If the loop configuration is asymmetric, then the energy may be radiated in an asymmetric way.  In that case, the loop will radiate and lose momentum as well as energy. In this paper, we obtain an analytic formula for the momentum radiated for any piecewise linear cosmic string loop.  In the center-of-mass frame, a cosmic string loop is specified by the position ${\\bf x}(t,\\sigma)$ of the string as a function of two variables: time $t$ and a space-like parameter $\\sigma$ that runs from $0$ to $L$.  The total energy of the loop is $\\mu L$ where $\\mu$ is the mass-per-unit-length of the string.  $L$ is referred to as the ``invariant length\" of the loop.  When gravitational back-reaction is neglected, the string loop satisfies equations of motion whose most general solution in the center-of-mass frame is \\begin{equation} {\\bf x}(t,\\sigma)= {1 \\over 2} \\big[ \\a(t+\\sigma) + \\b(t - \\sigma)\\big]. \\label{X} \\end{equation} Here $\\a(u) \\equiv \\a(u+L)$ and $\\b(v) \\equiv \\b(v+L)$ are a pair of periodic functions, satisfying the ``gauge condition\" $|\\a'(u)| = |\\b'(v)|=1$, where $'$ denotes differentiation w.r.t. the function's argument.  Because the functions $\\a$ and $\\b$ are periodic, each can be described by a closed loop.  These loops are referred to respectively as the $\\a$-loop and the $\\b$-loop.  Together, the $\\a$- and $\\b$-loops define the trajectory of the string loop.  If we define the four-momentum of the gravity waves emitted by a string loop to be $P^\\al=(E,P^i)$ where $i=x,y,z$, then the average rate of energy and momentum loss by an oscillating string loop is given by the four-vector $-\\P^\\al$, where \\begin{equation} \\P^\\al=(\\E,\\P^i) = \\gamma^\\al G \\mu^2 . \\label{P0} \\end{equation} Here $G$ is Newton's constant and we use units with $c=1$ and metric signature $(-,+,+,+)$.  Throughout this paper, a dot appearing over a symbol denotes the time derivative of that quantity.  In equation (\\ref{P0}), $\\E$ is the energy radiated (i.e., the power) and $\\P^i$ are the three spatial components of the momentum radiated, averaged over a single oscillation of the loop.  With our definition of $\\gamma^\\al$ and metric signature, the string loop is losing energy in the form of gravitational radiation when $\\gamma^0$ is positive (which is always the case).  Note that in reference \\cite{AllenCasper}, the quantity $\\gamma^0$ is denoted simply by $\\gamma$.  When one of the components of $\\gamma^i$ is positive, the loop is radiating a net amount of energy and momentum in that direction, and the loop itself will recoil and begin to accelerate in the opposite direction.  Thus if $\\gamma^x >0$ then the loop will begin to accelerate in the $-x$ direction.  The dimensionless quantities $\\gamma^\\al=(\\gamma^0,\\gamma^i)$ depend only upon the ``shape\" of the cosmic string loop.  That is, the energy and momentum radiated in gravitational radiation from a loop is invariant under a rescaling (magnification or shrinking) of the loop, provided that the velocity at each point on the rescaled loop is unchanged \\cite{Vilenkin,AllenShellard}.  Thus, without loss of generality, we consider only loops with invariant length $L=1$.  In a recent paper, we presented a new formula for $\\gamma^0$.  The formula is an exact analytic closed form for any piecewise linear cosmic string loop \\cite{AllenCasper}.  A piecewise linear loop is one which, at any time, is composed of straight segments each of which has constant velocity.  Equivalently, a piecewise linear loop is any loop for which the corresponding $\\a$- and $\\b$-loops are piecewise linear. As is shown in reference \\cite{AllenCasper}, the piecewise linear requirement is not very restrictive since in practice a smooth cosmic string loop may be well approximated by a piecewise linear loop with a moderately small number of segments $N$.  In the present paper, we show how the formula given in \\cite{AllenCasper} may be modified to give exact analytic closed form for the spatial momentum, $\\gamma^i$, as well as for $\\gamma^0$. The formula for the components of the momentum radiated are very similar to the formula for the radiated power.  In each case, the formulae is a sum of $O(N^4)$ terms, each of which involves nothing more complicated than log or arctangent functions.  Our C-code, which provides one implementation of the formulae, is publicly available via anonymous FTP from the directory pub/pcasper at the internet site alpha1.csd.uwm.edu.  The remainder of the paper is organized as follows.  Section \\ref{section2} explains how the formulae of reference \\cite{AllenCasper} may be modified to yield analytic, closed forms for the three spatial components of the radiated momentum.  This section generalizes the work done in section \\ref{section3} of reference \\cite{AllenCasper}.  The final steps of the solution which are described in sections IV-VI of reference \\cite{AllenCasper} are unchanged.  Thus, those sections are not repeated in this paper.  In section \\ref{section3} the resulting formula for both the radiated power and momentum is written explicitly for the case of a simple one-parameter family of string loops.  The values of $\\gamma^\\al$ for this family of loops are compared to those given by an independent numerical method as well as to the results given by our C-code implementation of the general formulas.  Excellent agreement is found in all cases.   The formula is then used to correct the small number of numerical values for the momentum radiated which appear in the existing literature.  These values are typically off by a factor of 2, though in some cases they are off by as much as a factor of 10. Section \\ref{section4} contains a catalog of $\\gamma^\\al$ values for some simple loop trajectories.  This is followed by a short conclusion. ",
        "conclusions": "\\label{conclusion}  We have modified the method of Allen and Casper \\cite{AllenCasper} to yield analytic closed-form results for the linear momentum radiated by piecewise linear cosmic string loops.  Any cosmic string loop can be arbitrarily well approximated by a piecewise linear loop with the number of segments sufficiently large.  An exact formula is given for a simple one-parameter family of string loops.  Our computer implementation of the general formula is then used to investigate the small number of numerical results published in the previous literature.  These results are found to be typically off by a factor of 2 from the correct results, though in some cases they are off by as much as a factor of 10.  A small catalog of loop trajectories and their $\\gamma^\\al$ values has been provided as a set of bench mark results for future analytic or numerical work.  Although the string loops studied in this paper are not physically realistic, they provide a simple set of trajectories with which to test our formula.  We intend to use the method of this paper to investigate a large sample of more physically realistic loop trajectories in the near future.     \\noindent \\vskip 0.3in \\centerline"
    },
    "9407/hep-ex9407003_arXiv.txt": {
        "abstract": "Higher order correlation measurements involve multiple event averages which must run over unequal events to avoid statistical bias. We derive correction formulas for small event samples, where the bias is largest, and utilize the results to achieve savings in CPU time consumption for the star integral. Results from a simple model of correlations illustrate the utility and importance of these corrections. Single-event correlation measurements such as in galaxy distributions and envisaged at RHIC must take great care to avoid this unnecessary pitfall. ",
        "introduction": "\\label{sec:intro}   In the hope of obtaining new insights into the old problem of soft interactions in high energy physics, there has been much interest in multiparticle correlations in the last few years, spurred by new theoretical perspectives and a large amount of multiparticle data in hadronic and nuclear collisions \\cite{Bia86a,DeW93a}. While various Monte Carlo codes and analytical models often yield very similar behavior in rapidity and $p_\\perp$ distributions, they predict widely differing particle correlations. Experimentally measured correlations are therefore becoming an important and severe test of such theoretical models.   Experience has shown, however, that correlation measurements require considerably more subtle and sophisticated understanding of statistics than single-particle quantities do, and there has been much improvisation in methodology and interpretation of data. A clean and consistent statistical basis for such methodology has become a matter of urgency.   Recently, we have shown how, through the use of the correlation integral, the measurement of multiparticle correlations can be greatly improved, both in conventional variables such as rapidity and azimuthal angle \\cite{Egg93a} and in terms of relative momenta used in pion interferometry \\cite{Egg93d}. By deriving all quantities from first principles, our techniques, besides greatly improving the accuracy of correlation measurements, permit for the first time the direct measurement of cumulants. Moments, while easily measured, contain lower-order correlations. Cumulants, testing the actual correlations, are to be preferred, but they are hard to implement for at least two reasons: they contain a hidden statistical bias and are expensive in terms of CPU time.   The mentioned bias is present in {\\it all} correlation measurements; it is large for small data samples and strong correlations while becoming negligible for large samples and weak correlations. Our analysis provides the framework for understanding and dealing with this bias in any present or future data set.   Secondly, correlation integral algorithms, while much superior to conventional methods, run at least as the square  of the event multiplicity and the sample size $N_{\\rm ev}$. In understanding this bias, we point the way to huge reductions in computer time also. Defining for inner event averages a ``reduced sample average'' containing only $A$ events, and correcting for the resulting bias, we obtain, compared to full event mixing, savings of a factor $N_{\\rm ev}/A$ for the star integral. For a typical case with $N_{\\rm ev} = 10^5$ events and $A=100$, the savings amount to a factor $1000$ over full event mixing.   Besides the bias under discussion, there clearly are other biases, both statistical and systematic, which greatly influence multiparticle correlations. Typical unwanted but often important effects include the ``empty bin effect'' \\cite{Lip91a} and contamination by trivial sources of particle correlations such as Dalitz decays and gamma conversion \\cite{EMU01-92a} or the misidentification of pieces of a single track as two (highly correlated) particles \\cite{Lip90a}. All these have been shown to be capable of drowning other correlations in the background. Eliminating such biases is therefore a {\\it sine qua non} of multiparticle correlations. We take here a simple model of such correlations, the split track model \\cite{Lip91b}, to illustrate both the use of the reduced event average with bias correction and the effect such contamination may have on correlation data.   In Section \\ref{sec:uprod}, we first explain the use and significance of unbiased estimators and find a general form for unbiased estimators of products of densities. We develop the general formalism in Section \\ref{sec:corterms} and apply these in Section \\ref{sec:starc} to the star integrals. An example of behavior of the star integral as applied to the split track model is given in Section \\ref{sec:splt}, followed by an outline of  steps needed to measure unbiased correlations in truly small samples and a brief discussion of corrections for other correlation methods. We conclude with some comments on small samples and single-event measurements. First results regarding unbiased estimators can be found in Ref.\\ \\cite{Kra93}. More recently, this formalism has been applied to the problem of normalization in a fixed-bin context \\cite{KS94}. ",
        "conclusions": "The statistical bias arising through the need for multiple event averages must be understood and corrected for. We have shown how the theory of unbiased estimators leads to correction formulas for the star integral, thereby making it possible to run it under fast algorithms without loss in accuracy. For the envisaged large data samples, this savings in CPU time may prove the difference between viability and impossibility of correlation measurements in future.   For truly small samples, the correction for this bias is not a tool for faster analysis but constitutive for a correct measurement. Typical small samples are found in cosmic ray data and in galaxy correlations as well as the subdivision of inclusive data samples into fixed-multiplicity subsamples. All these must take cognizance of the bias and correct for it.    This brings us to the subject of single-event measurements: event mixing is, of course, not possible when there is just one available. For the proposed measurement of Bose-Einstein correlations in single events in nuclear collisions at RHIC and LHC, the solution is clearly to normalize by event mixing based on a sample of similar events. Most notably, this mixing sample should have the same multiplicity and general characteristics; such requirements will necessarily restrict the sample to relatively few events, so that the bias corrections may become important.    Galaxy distributions, on the other hand, present a much more difficult task: there is no pool of big bang events to make up the uncorrelated background. So far, the preferred solution was to assume a uniform distribution on a sufficiently large scale. Recent results on the large-scale structure of the universe, however, make this assumption increasingly untenable. The only alternative route would appear to be to select a number of windows in the sky (with about the same overall galaxy count as the window used for the numerator) and, neglecting the long-range correlations, count these as different ``events''. In this way, no assumption of overall uniformity need be made."
    },
    "9407/astro-ph9407015_arXiv.txt": {
        "abstract": "%  We model the temperature distribution at the surface of a magnetized neutron star and study the effects on the observed X-ray spectra and light curves. General relativistic effects, i.e., red-shift and lensing, are fully taken into account. Atmospheric effects on the emitted spectral flux are not included: we only consider blackbody emission at the local effective temperature. In this first paper we restrict ourselves to dipolar fields. General features are studied and compared with the {\\em ROSAT} data from the pulsars 0833-45 (Vela), 0656+14, 0630+178 (Geminga), and 1055-52, the four cases for which there is strong evidence that thermal radiation from the stellar surface is detected.   The composite spectra we obtain are not very different from a blackbody spectrum at the star's effective temperature. We conclude that, as far as blackbody spectra are considered, temperature estimates using single temperature models give results practically identical to our composite models. The change of the (composite blackbody) spectrum with the star's rotational phase is also not very large and may be unobservable in most cases.   Gravitational lensing strongly suppresses the light curve pulsations. If a dipolar field is assumed, pulsed fractions comparable to the observed ones can only be obtained with stellar radii larger than what predicted by current models of neutron star structure, or with low stellar masses. Moreover, the shapes of the theoretical light curves with dipolar fields do not correspond to the observations. The use of magnetic spectra may rise the pulsed fraction sufficiently, but will certainly make the discrepancy with the light curve shapes worse: dipolar field are not sufficient to interpret the data. Many neutron star models with a meson condensate or hyperons predict very small radii, and hence very strong lensing, which will require highly non dipolar fields to be able to reproduce the observed pulsed fractions, if possible at all: this may be a new tool to constrain the size of neutron stars.    The pulsed fractions obtained in all our models increase with photon energy: the strong decrease observed in Geminga at energies 0.3 - 0.5 keV is definitely a genuine effect of the magnetic field on the spectrum in contradistinction to the magnetic effects on the surface temperature considered here. Thus, a detailed analysis of thermal emission from the four pulsars we consider will require both complex surface field configurations and the inclusion of magnetic effects in the atmosphere (i.e., on the emitted spectrum). ",
        "introduction": "%  The detection of thermal emission from the surface of a neutron star is one of the `Holy Graal's of X-ray astronomy. At the first detection of X-rays from the direction of the Crab supernova remnant, surface thermal radiation from the neutron star already expected to be present in this remnant was proposed as the most probable source (Bowyer \\etal 1964), but the claim was soon disproved and even the most recent {\\em ROSAT} observation of the Crab pulsar failed to detect any emission from the surface (Becker \\& Aschenbach 1993). A compilation of all {\\em Einstein} observations (Seward \\& Wang 1988) listed ten neutron stars detected in soft X-rays, to which should now be added Geminga which at that time was not yet proved to be a neutron star but had been clearly seen by {\\em Einstein} (Bignami, Caraveo \\& Lamb 1983). As of August 1993 there were thirteen confirmed detections of pulsars by {\\em ROSAT} and six unconfirmed ones (\\\"{O}gelman 1993). In most cases the radiation is probably of magnetospheric origin with some contamination from the surrounding synchrotron nebula, at least for the younger candidates, and surface thermal emission in some cases. With the sensitivity of the {\\em ROSAT}'s PSPC (Position Sensitive Proportional Counter) and long exposure times there is now strong spectral evidence that thermal radiation has been detected from four neutron stars (\\\"{O}gelman 1993): PSR 0833-45 (Vela) (\\\"{O}gelman, Finley  \\& Zimmermann 1993), PSR 0656+14 (Finley, \\\"{O}gelman \\& Kizilo\\u{g}lu 1992), PSR 0630+178 (Geminga) (Halpern \\& Holt 1992), and PSR 1055-52 (\\\"{O}gelman \\& Finley 1993). Moreover, these four objects show pulsed X-ray emission, three of them (except Geminga) are radio pulsars and three (except PSR 0656+14) have also been detected as $\\gamma$-ray pulsars.   Earlier {\\em Einstein} observations had already provided some limited evidence for detection of surface thermal radiation in the cases of the Vela pulsar (Harnden \\etal 1985), PSR 0656+14 (C\\'{o}rdova \\etal 1989), and Geminga (Halpern \\& Tytler 1988), while in the case of PSR 1055-52 (Cheng \\& Helfand 1983) thermal emission was considered as incompatible with the data. In later {\\em EXOSAT} observations, with broad band spectroscopy only, thermal radiation was considered as the most reasonable origin of the detected soft X-rays in both cases of the Vela pulsar (\\\"{O}gelman \\& Zimmermann 1989) {\\em and} PSR 1055-52 (Brinkmann \\& \\\"{O}gelman 1987). Because of its late discovery, as an X-ray source, in the {\\em Einstein} data base, PSR 0656+14 has not been observed by {\\em EXOSAT}. The {\\em EXOSAT} observation of Geminga (Caraveo \\etal 1984) did not give any new spectral information compared to the {\\em Einstein} results. A review of the pre-{\\em ROSAT} observational situation has been given by \\\"{O}gelman (1991).   The quality of the {\\em ROSAT} data from these four nearby neutron stars presents a new chalenge for theorists to provide good models for their interpretation. The heretofore published analyses of these data have all assumed a unique surface temperature, with at most a second thermal component coming from the small hot polar caps. We model here the temperature distribution at the surface of a magnetized neutron star and study its effects on the received spectra and light curves. The crustal magnetic field affects the heat transport in the layers beneath the surface and makes that regions of the star where the field is almost normal to the surface will be warmer than regions where the field is almost tangential to the surface. These temperature differences will give rise to modulation of the received flux at energies between 0.1 and 1 keV and are a natural explanation for the observed pulsations in the above mentioned four neutron stars. This long searched for detection of thermal radiation from the surface of neutron stars thus opens up a new window in the study of these objects. It has the potential to tell us about the structure of the surface magnetic field and give us new information about the size of these stars through gravitational lensing effects which obviously will be substantial. Our purpose in this first paper is to present the general physics involved and study the simplest case of a dipolar surface magnetic field. We have tried to present as clearly as possible the underlying physical ingredients as well as the method used, laying hopefully a clear groundstone for future improvements and/or modifications.   General relativistic effects may be enormous in neutron stars and we take fully into account both gravitational red-shift and gravitational lensing. Magnetic fields are also affected by strong gravitational fields but we do not consider this effect: of critical importance for the surface temperature distribution is the angle between the surface's normal and the magnetic field, and this angle is practically unaffected by gravity (Ginzburg \\& Ozernoy 1964). The major effect of gravity on the surface magnetic field is to increase its strength at small radii: for a given dipolar field at infinity the surface strength is increased by 20-50\\% by gravity compared to the value it would have in flat space-time. The surface field strengths we consider should thus simply be somewhat reduced for comparison with values obtained for example from pulsar spin-down. Our results are however not very sensitive to changes of this size in the field strength. We do not include the effects of the magnetic field on the atmosphere where the emitted spectrum is determined. These effects are also substantial and will hopefully be included in future work.   It has been proposed that the surface of neutron stars may be a magnetic solid (Ruderman 1974; Chen, Ruderman \\& Sutherland 1974). Even if improved calculations of the atomic lattice cohesive energy in very strong magnetic fields have indicated that this is not the case (Jones 1986), one should nevertheless keep in mind this possibility. It would obviously have dramatic effects on the emitted spectrum (Brinkmann 1980) and some, comparatively smaller, effect on the surface temperature (see Van Riper 1988 for simple estimates) Our model is based on magnetized envelope calculations which assume that the surface is not a magnetic solid: would this be uncorrect, our results should clearly be reconsidered.   We must also mention that the interpretation presented here assumes that the surface temperature is determined by the flow of heat from the star's interior and thus carries the imprint of the underlying crustal magnetic field. Another interpretation has been proposed (Halpern \\& Ruderman 1993) in which the hard X-rays emitted by the hot polar caps are scattered back onto the surface by the magnetospheric plasma: if this is the case the surface temperature has nothing to do with the properties of the magnetized envelope and our model is then obviously irrelevant. A composite model is also possible: the general temperature distribution may be determined by the heat flow from the interior and some regions heated by the back scattered hard X-rays. Moreover, absorption and scattering of radiation by the surrounding magnetospheric plasma may also be an important factor in reshaping the emitted flux (Halpern \\& Ruderman 1993). Which of these possibilities is actual can only be determined by studying each of them carefully. This paper is a first step in that direction.   The structure of the paper is a follow. The {\\em ROSAT} data are summarized in \\S~\\ref{sec:data} where we emphasize the features relevent to our purpose. In \\S~\\ref{sec:tbts} we describe the effects of the magnetic field on heat transport in the envelope and our model for the surface temperature distribution and in \\S~\\ref{sec:litc_sp} we present the method used to calculate the fluxes as observed by {\\em ROSAT}. Our results are in \\S~\\ref{sec:results} and they are discussed in \\S~\\ref{sec:disc}, followed by our conclusions in \\S~\\ref{sec:concl} ",
        "conclusions": "}%   The simple model presented here, with dipolar fields, shows several features similar to the observed ones but with significant shortcomings. We obtain pulsed fractions which are lower that the observed ones, unless very large radii or very low masses are assumed. The shape of the light curves do not match the observations, indicating the presence of deviations from a purely dipolar field, the strength of the required correction depending on the assumed geometry and the size of the star. One can, however, reasonably expect that more complicated field structure will be able to reproduce the observed pulsed fractions and the shapes of the light curves: there is probably no need to invoke external heating of the surface and/or magnetospheric absorption (see Introduction) to reproduce the data, but this does not mean that these processes are not present. `Energy dependent pulse shapes and phases are trying to tell us the whole story; we have to interpret them' (\\\"{O}gelman 1993), but deciphering the story will not be easy. A complete model will have to consider complex surface fields and also include the magnetic effects in the atmosphere."
    },
    "9407/astro-ph9407084_arXiv.txt": {
        "abstract": "We present the light curve of an unusual variable object, OGLE~\\#7, detected during the OGLE search for microlensing events. After one season of being in a low, normal state, the star brightened by more than 2~mag with a characteristic double-maximum  shape, and  returned to normal brightness after 60 days. We consider  possible explanations of the photometric behavior of OGLE~\\#7. The binary microlens model seems to be the most likely explanation -- it reproduces well the observed light curve and explains the observed colors of OGLE~\\#7. The characteristic time scale of the OGLE~\\#7 event, $t_E$, is equal to 80 days, the longest observed to date. The binary microlens model predicts that the spectrum of the star should be composite, with roughly 50\\% of its light in the $I$-band coming from a non-lensed source. ",
        "introduction": "The Optical Gravitational Lensing Experiment (OGLE) is a long term observing  project with the main goal of searching for dark  matter in our Galaxy using microlensing (Paczy\\'nski 1986). After two years of continuous monitoring of approximately two million non-variable stars in the direction of the Galactic bulge, ten microlensing events have been detected (Udalski et al. 1993b, Udalski et al. 1994a,  Udalski et al. 1994b). The resulting optical depth of microlensing  $(3.3 \\pm 1.2) \\times 10^6$ is higher than previous theoretical estimates and indicates that the bulge of our Galaxy is in fact a bar, with its long axis inclined $ \\sim 15 $ degrees to the line of sight (Paczy\\'nski et al. 1994b).  A microlensing event caused by a single, point-like lensing object has an achromatic light curve  with a well defined, characteristic shape which is symmetric around the maximum of brightness (Paczy\\'nski 1986, 1991). The lensing phenomenon should  not repeat as the probability of the same star being lensed twice is negligible. All the OGLE microlensing events except OGLE~\\#7 displayed such photometric behaviors (for OGLE \\#6, a better fit to the data can be obtained with a binary microlens model, however, the case is not strong, Mao \\& Di~Stefano 1994). All the reported MACHO (Alcock et al. 1994) and EROS (Aubourg  et al. 1993) events can also be well fit by single lenses.  It is well known that majority of stars are found in binary or multiple systems (Abt 1983).  Therefore it is natural to expect some microlensing events to be caused by binary systems. The light curve of such events might be considerably different from that of single microlens events and would depend on the geometry of lensing (Mao \\& Paczy\\'nski 1991, Mao \\& Di~Stefano 1994). Light curve may also exhibit  color variations, although these may be difficult to detect because of small amplitude.  One of the OGLE microlensing candidates found during the OGLE search, OGLE \\#7, exhibits very unusual light variations which do not resemble variations of any known variable stars. On the other hand, the light variations are strikingly similar to the theoretical light curves possible for binary microlenses (Mao \\& Paczy\\'nski 1991). In this {\\it Letter} we present a detailed analysis of the variability of OGLE \\#7 candidate, emphasizing binary microlensing as a possible explanation of observed light variations. Section 2 describes details of the observations, Section 3, the OGLE \\#7 light curve and Section 4, possible explanations of its photometric behavior.  We conclude the paper with a discussion in Section 5.  \\clearpage ",
        "conclusions": "In the previous section we considered possible explanations of the strange photometric behavior of OGLE~\\#7. It seems that the binary microlens model is the most likely explanation, as the model reproduces well the light variations and explains the observed colors of the star. However, we cannot rule out the possibility that we have  discovered a completely new type of variable star, and that the binary microlens model is simply a false positive (cf. Mao \\& Di~Stefano 1994). However, such a false positive seems unlikely.  Generally speaking, there may be multiple binary lens fits to a given light curve, especially one with weak (small amplitude) lensing signature (Mao \\& Di~Stefano 1994). Fortunately, OGLE \\#7 is a very strong event (brightening by more than two  magnitudes) with distinctive features; correspondingly the models are well constrained.  The best model presented here is  significantly better than any other fits we have found. We believe that it is probably the unique solution in the multiple dimensional parameter space. Our model not only provides a good fit to the somewhat sparsely sampled light curve, it also makes a very specific prediction, i.e., the spectrum should be a composite of at least two sources of comparable brightness. If the extra light in our model is contributed by an additional source close to the lensed star, then the additional source is likely to have a different radial velocity from the lensed star. The velocity difference may not be large, therefore high dispersion instruments (e.g., Keck telescope) are needed. On the other hand, if the binary lens contributed  the extra light, then the circular motion of the two components ($\\sim 10\\kms$) can be measured spectroscopically. This will in turn reliably determine the other parameters (including the lens mass) in our model. There is one more test which distinguishes the lensing model from other kinds of variability. The microlensing event should not repeat, as the probability of the same star being microlensed more than once is practically zero. Thus if brightening of OGLE~\\#7 repeats, then  the microlens model will have to be rejected. To summarize, all the observations are fully consistent with the binary microlens model; our model can be further tested by high dispersion spectroscopic observations from the ground, by  high resolution imaging with HST and by future long-term monitoring of the source. If future observations contradict the prediction of the binary scenario, then more elaborate models will have to be invented, a possibility we choose not to pursue here.  The theoretical estimate that 10\\% of the events may exhibit binary features (Mao \\& Paczy\\'nski 1991) was based on the binary population study of the solar neighborhood. However, it is conceivable that the fraction could be higher if the stellar population in the bulge is different. Binary light curves are usually very bright (OGLE \\#7 reaches 15~mag in the $I$ band), therefore these events can be more easily detected than single lens events. With the implementation of the early warning system of OGLE (Paczy\\'nski 1994), most of these binary events can be caught in the early stages and therefore be well sampled in the bright caustic crossing phase. For the microlens model of OGLE \\#7, the caustic crossing lasted for only $5 \\times R_\\star/(5R_\\odot)$ hours. This indicates that frequent sampling is extremely important. A densely sampled caustic crossing event will allow us to resolve the structure of the source more easily than for the case of a single lens (Gould 1994; Nemiroff \\& Wickramasinghe 1994; Witt \\& Mao 1994). In addition, relatively small changes in the lensing parameters will induce large change in the light curve; therefore, a well sampled binary lens light curve offers the hope that all of the parameters can be determined accurately, including the mass of the lenses.  Photometry of OGLE~\\#7 and other microlensing events, as well as a regularly updated OGLE status report can be found over the Internet at host ``sirius.astrouw.edu.pl'' (148.81.8.1), using the ``anonymous ftp'' service (directory ``ogle'', files ``README'', ``ogle.status'', ``early warning''). The status report contains the latest news and references to all the OGLE related papers, and the PostScript files of some publications. Information on the recent OGLE status is also available via  ``World Wide Web'' WWW: ``http://www.astrouw.edu.pl/''."
    },
    "9407/gr-qc9407007_arXiv.txt": {
        "abstract": "\\noindent All regular and singular cosmological perturbations in a radiation dominated Einstein-de Sitter Universe with collisionless particles can be found by a generalized power series ansatz. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9407/astro-ph9407036_arXiv.txt": {
        "abstract": "A local void in the globally Friedmann-Robertson-Walker (FRW) cosmological model is studied. The inhomogeneity is described using the Lema\\^{\\i}tre-Tolman-Bondi (LTB) solution with the spherically symmetric matter distribution based on the faint galaxies number counts. We investigate the effects this has on the measurement of the Hubble constant and the redshift--luminosity distance relation for moderately and very distant objects ($z \\approx 0.1$ and more). The results, while fully compatible with cosmological observations, indicate that if we happened to live in such a void, but insisted on interpreting cosmological observations through the FRW model, we could get a few unexpected results. For example the Hubble constant measurement could give results depending on the separation of the source and the observer. ",
        "introduction": "It seems, particularly after the introduction of the inflationary paradigm (\\guth), that the isotropic and homogeneous Friedmann-Robertson-Walker (FRW)  cosmological models are best suited for the description of the global structure and the evolution of the universe. However, a similar statement is not necessarily true when cosmologically moderate scales are thought of.   There exists direct observational evidence in favour of the large scale isotropy of the observed universe, namely, the COBE data confirming a high degree of isotropy of the cosmic microwave background radiation (CMBR) (\\cobe; \\COBE). However, the observational basis for the other standard assumption made in the FRW cosmology, the homogeneity, is weaker. There exists observational evidence in favour of larger and larger structures (e.g. \\lstr; \\grwall).   We think that there exists sufficient observational evidence (discussed later in this paper) to support a conjecture that we may live in a relatively large underdense region embedded in a globally FRW universe. Exploring observational properties of such a model is the aim of the present paper.   The simple model presented in this paper is restricted by the two physical demands we impose on it. Firstly, to be consistent with the CMBR isotropy it has to be spherically symmetric. Secondly, the model should be very similar to an FRW one at the beginning of the expansion, but become observably different at later times. In this manner, we could retain the accomplishments of the FRW cosmology in dealing with early epochs, while gaining new freedom in modelling the more recent universe.   The work on modelling voids of the Lema\\^{\\i}tre-Tolman-Bondi type \\footnote{A cosmological solution spherically symmetric about one point was first proposed by Lema\\^{\\i}tre (\\lem). However, it is usually called the Tolman--Bondi solution (\\tol, \\bon).} in the expanding FRW universe has been extensive. Main results and references will be briefly discussed later. (An excellent review of the inhomogeneous cosmology exists: \\krasb.) Nevertheless, the observable consequences of such a model have seldom been studied (e.g. \\pacz; \\motat).   In the following section, we briefly describe the LTB model. Section \\ref{void} consists of a concise review of the main results in modelling LTB voids, a discussion of the observational background and the simple model of a local void presented here. The description of our results of numerical calculations is contained in Section \\ref{resnum} The closing section contains a discussion and conclusions.   Throughout this paper we use units in which $G=c=1$, unless stated otherwise. Moreover, we choose the cosmological constant $\\Lambda=0$. ",
        "conclusions": "\\label{discuss}   The LTB voids presented here decrease their density contrasts (the depth of the void with respect to the FRW background) when evolved back in time. At early times they are almost homogenized: at $t/(t_0+\\beta_0) \\simeq 10^{-6}$ we have $|{\\rho}_{LTB}(r)/{\\rho}_{FRW}-1| \\simeq 10^{-5}$ everywhere. This corresponds to a universe which at the beginning is very similar to the FRW one, but different at late stages.   In a model utilizing a local LTB void, while retaining the accomplishments of the FRW cosmology in dealing with epochs preceding the matter dominated era, we can gain new freedom in modelling the more recent universe. We can solve the age of the universe problem by assuming $\\beta(r) = const \\neq 0$, provide the excess power observed on scales of 5---10,000 km s$^{-1}$ in modelling structure formation (see \\motat) and provide an explanation for the wide range of reported values of the Hubble constant.   The use of a locally inhomogeneous model enriches the spectrum of available interpretations. The ultimate question to be addressed, however, is the agreement between predictions of the model and observations. As has been demonstrated by the results of the present work, the observationally based density distributions spanning the range of $\\Omega \\in (0.2;1)$ satisfy the observational tests. The agreement with observations is achieved both in the case of the model with the ``age of the universe''  equal to that of the critical ($\\Omega_0 = 1$) FRW one and the ``older'' case with $t_0+\\beta_0$ equal to the FRW $\\Omega_0=0.2$ value. Theoretical prejudice (as powerful as the inflationary paradigm) might favour the critical FRW model."
    },
    "9407/astro-ph9407060_arXiv.txt": {
        "abstract": "I give a general formulation of the constraints on models of inflation ended by a first order phase transition arising from the requirement that they do not produce too many large (observable) true vacuum voids -- the `big bubble problem'.  It is shown that this constraint can be satisfied by a simple model in Einstein gravity -- a variant of `hybrid' or `false vacuum' inflation. ",
        "introduction": " ",
        "conclusions": ""
    },
    "9407/astro-ph9407055_arXiv.txt": {
        "abstract": "Starlight from distant galaxies ($z > 3$) is redshifted into the near infrared band with observed wavelengths from 2-8 $\\mu$m.  Most of the light is emitted by stars that have a peak emission at the 1.6 $\\mu$m wavelength of the minimum of the H$^-$ opacity.  We present simulated images of galaxy and star fields at 3, 4.7 and 8 $\\mu$m, using the expected performance of the infrared camera on the Space InfraRed Telescope Facility (SIRTF). Standard astronomical image processing tools are used to locate sources, distinguish stars from galaxies, and create color-magnitude and color-color diagrams for the galaxies. ",
        "introduction": "The following steps have been taken in generating and analyzing the SIRTF images.  The galaxy population in these images was generated in clusters with redshifts ranging from 0 to 10.  Clusters were assumed to form with an exponential distribution of formation times having a mean time of formation corresponding to $z=5$ in an $H_\\circ = 50$, $\\Omega = 1$ cosmology.  The density of galaxies has been increased slightly over the value given by Schechter in order to match Cowie's deep K-band counts. Luminosities and colors evolve using Bruzual $\\mu$-models with a $\\mu$ that depends on galaxy type.  Stars were added to the images using the populations used by Elias. Brown dwarfs are also included, but because we have assumed only old cold brown dwarfs ($M = 0.05\\;M_\\odot, \\; t = 10^{10}\\;{\\rm yrs}, \\; T_{color} = 462 \\; {\\rm K}, \\; L = 10^{-6} L_\\odot$), none of the detected sources were brown dwarfs.  Of the 32 stars in the field brighter than 0.1 $\\mu$Jy at 4.7 $\\mu$m, 6 are brown dwarfs, but the brightest is just fainter than the 4.7 $\\mu$m flux limit at 0.6 $\\mu$Jy.  Its 8 $\\mu$m flux is 1.5 $\\mu$Jy which is under the 8 $\\mu$m limit as well.  Note that the color is redder than any of the galaxies that we do detect.  Galaxy spectra are based on the spectral energy distributions for ellipticals and spirals by Marcia Rieke, which were combined with various weights to match Bruzual $\\mu$-models in the optical. This allowed us to include the broad IR features due to the H$^-$ opacity minimum.  This peak at 1.6 $\\mu$m rest wavelength can be seen in the bluing of the 4.7:8 $\\mu$m color at $z = 2$.   800$\\times$800 pixels images covering 5.3333$^\\prime$ were generated, and then convolved with the SIRTF beam.  We assumed the diffraction limit of an 85 cm telescope with a 30\\% linear obscuration.  In order to not exceed the SIRTF specification of 50\\% encircled energy in a 2$^{\\prime\\prime}$ diameter circle, this diffraction-limited beam was further convolved with a 1.657$^{\\prime\\prime}$ FWHM Gaussian.  These 800$\\times$800 pixel images with 0.39$^{\\prime\\prime}$ pixels were then made into 256$\\times$256 pixel images with 1.17$^{\\prime\\prime}$ pixels by summing 3$\\times$3 blocks of pixels.  This array was sub-stepped across the field in a 3$\\times$3 pattern giving a final picture with 768$\\times$768 pixels of size 1.17$^{\\prime\\prime}$ on 0.39$^{\\prime\\prime}$ centers. Noise was added to each pixel in this image, using the following noise levels: 3 $\\mu$m, 20.4 nJy, corresponding to 2500 seconds; 4.7 $\\mu$m, 74 nJy, corresponding to 2500 seconds; 6.2 $\\mu$m, 155 nJy, corresponding to 10,000 seconds; and 8 $\\mu$m, 217 nJy, corresonding to 10,000 seconds. Because of the 3$\\times$3 substepping, a total of 9 frames at each wavelength are needed, giving a total exposure time of 22500+22500+90000 seconds or 1.6 days for the image shown.  The first step after getting the 3$\\times$3 sub-stepped images is to smooth with a 3$\\times$3 box. These images were written out as FITS files and displayed by SAOIMAGE. The RGB image was created using a FORTRAN program to convert the intensities into a PPM (Portable Pixel Map) file which was converted into a JPEG file using xv, and then printed to a HP Deskjet 1200C printer using Adobe Photoshop. Prints were also obtained using a Kodak XL 7700 dye sublimation printer and a Polaroid Palette film recorder. ",
        "conclusions": "The SIRTF image quality is marginal for discriminating between galaxies and stars.  The low-$z$ clump of sources with high $F[1.95^{\\prime\\prime}]/F[2.73^{\\prime\\prime}]$ ratios are stars, but several galaxies have higher ratios and thus appear more compact than some of the stars.  Fortunately almost all the faint sources in a high latitude deep survey will be galaxies.  Photometric redshifts using colors out to $\\lambda = 8\\;\\mu$m appear to be reliable. There are 40 galaxies with $z > 3$ in the sample of 346 sources. Sorting the 346 sources by 4.7:8 $\\mu$m color, the 41 reddest sources contain 39 out of these $z > 3$ galaxies. The 4.7:8 $\\mu$m color redshift diagram appears to be saturating at $z = 5$. The 3:4.7 $\\mu$m color saturated at $z = 2$ and then became bluer for higher redshifts, so the longer wavelength data is needed for reliable photometric redshifts at high $z$."
    }
}