Search

Particle production in cosmology is often efficiently computed in terms of Bogoliubov transforms. Restricting to a particular class of dispersion relationships, we identify a map between the number of particles produced in a special kinematic limit and a Stokes phenomena related topology of analytic continuation of the Bogoliubov coefficient functions. Intuitively, this kinematic limit corresponds to the long wavelength limit although a more precise description depends on the nature of the curved spacetime. To identify the topology, we reformulate the usual Bogoliubov computations as a type of SU(1,1) gauged differential equation and utilize a special gauge together with a discrete symmetry that naturally characterizes the dispersion relationship. Using a dark matter model and a nonzero constant spatial curvature model, we estimate how such topological contributions will arise in physical applications., Comment: 42 pages + appendices and references, 8 figures

Previous numerical investigations of gravitational particle production during the coherent oscillation period of inflation displayed unexplained fluctuations in the spectral density of the produced particles. We argue that these features are due to the quantum interference of the coherent scattering reactions that produce the particles. We provide accurate analytic formulae to compute the particle production amplitude for a conformally-coupled scalar field, including the interference effect in the kinematic region where the production can be interpreted as inflaton scattering into scalar final states via graviton exchange., Comment: 19 pages + appendices and references, 3 figures, v2 - references added, matches JHEP

Analytic and numerical techniques are presented for computing gravitational production of scalar particles in the limit that the inflaton mass is much larger than the Hubble expansion rate at the end of inflation. These techniques rely upon adiabatic invariants and time modeling of a typical inflaton field which has slow and fast time variation components. A faster computation time for numerical integration is achieved via subtraction of slowly varying components that are ultimately exponentially suppressed. The fast oscillatory remnant results in production of scalar particles with a mass larger than the inflationary Hubble expansion rate through a mechanism analogous to perturbative particle scattering. An improved effective Boltzmann collision equation description of this particle production mechanism is developed. This model allows computation of the spectrum using only adiabatic invariants, avoiding the need to explicitly solve the inflaton equations of motion., Comment: 37 pages, 5 figures

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of u(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an $S_4$ permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.

Through a mechanism similar to perturbative particle scattering, particles of mass $m_\chi$ larger than the Hubble expansion rate $H_\mathrm{inf}$ during inflation can be gravitationally produced at the end of inflation without the exponential suppression powers of $\exp(-m_\chi/H_\mathrm{inf})$. Here we develop an analytic formalism for computing particle production for such massive particles. We apply our formalism to specific models that have been previously been studied only numerically, and we find that our analytical approximations reproduce those numerical estimates well., Comment: v2: 24 pages, 1 figure. Refs added. Clarified discussion of time scales at Eq. (6.11)

Basis tensor gauge theory (BTGT) is a reformulation of ordinary gauge theory that is an analog of the vierbein formulation of gravity and is related to the Wilson line formulation. To match ordinary gauge theories coupled to matter, the BTGT formalism requires a continuous symmetry that we call the BTGT symmetry in addition to the ordinary gauge symmetry. After classically interpreting the BTGT symmetry, we construct using the BTGT formalism the Ward identities associated with the BTGT symmetry and the ordinary gauge symmetry. As a way of testing the quantum stability and the consistency of the Ward identities with a known regularization method, we explicitly renormalize the scalar QED at one-loop using dimensional regularization using the BTGT formalism., Comment: 23 pages

We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory., Comment: 25 pages

Isocurvature perturbations in the inflationary literature typically involve quantum fluctuations of bosonic field degrees of freedom. In this work, we consider isocurvature perturbations from fermionic quantum fluctuations during inflation. When a stable massive fermion is coupled to a non-conformal sector different from the scalar metric perturbations, observably large amplitude scale invariant isocurvature perturbations can be generated. In addition to the computation of the isocurvature two-point function, an estimate of the local non-Gaussianities is also given and found to be promising for observations in a corner of the parameter space. The results provide a new class of cosmological probes for theories with stable massive fermions. On the technical side, we explicitly renormalize the composite operator in curved spacetime and show that gravitational Ward identities play an important role in suppressing certain contributions to the fermionic isocurvature perturbations., Comment: 51 pages, 4 figures

Sources of isocurvature perturbations and large non-Gaussianities include field degrees of freedom whose vacuum expectation values are smaller than the expansion rate of inflation. The inhomogeneities in the energy density of such fields are quadratic in the fields to leading order in the inhomogeneity expansion. Although it is often assumed that such isocurvature perturbations and inflaton-driven curvature perturbations are uncorre- lated, this is not obvious from a direct computational point of view due to the form of the minimal gravitational interactions. We thus compute the irreducible gravitational contributions to the quadratic isocurvature-curvature cross-correlation. We find a small but non-decaying cross-correlation, which in principle serves as a consistency prediction of this large class of isocurvature perturbations. We apply our cross-correlation result to two dark matter isocurvature perturbation scenarios: QCD axions and WIMPZILLAs. On the technical side, we utilize a gravita- tional Ward identity in a novel manner to demonstrate the gauge invariance of the computation. Furthermore, the detailed computation is interpreted in terms of a soft-{\zeta} theorem and a gravitational Ward identity. Finally, we also identify explicitly all the counterterms that are necessary for renormalizing the isocurvature perturbation composite operator in inflationary cosmological backgrounds., Comment: 41 pages, 2 figures

We propose a group theoretic condition which may be applied to extensions of the Standard Model in order to locate regions of parameter space in which the electroweak phase transition is strongly first order, such that electroweak baryogenesis may be a viable mechanism for generating the baryon asymmetry of the universe. Specifically, we demonstrate that the viable corners of parameter space may be identified by their proximity to an enhanced discrete symmetry point. At this point, the global symmetry group of the theory is extended by a discrete group under which the scalar sector is non-trivially charged, and the discrete symmetry is spontaneously broken such that the discrete symmetry relates degenerate electroweak preserving and breaking vacua. This idea is used to investigate several specific models of the electroweak symmetry breaking sector. The phase transitions identified through this method suggest implications for other relics such as dark matter and gravitational waves., Comment: 17 pages, 4 figures

Gravitational particle production naturally occurs during the transition from the inflationary phase to the non-inflationary phase. If the particles are stable and very weakly interacting, they are natural nonthermal dark matter candidates. We show that such nonthermal dark matter particles can produce local non-Gaussianities large enough to be observed by ongoing and near future experiments without being in conflict with the existing isocurvature bounds. Of particular interest is the fact that these particles can be observable through local non-Gaussianities even when they form a very small fraction of the total dark matter content., Comment: 18 pages, 4 figures, version accepted by PRD

We revisit the gravitational production of massive Dirac fermions in inflationary cosmology with a focus on clarifying the analytic computation of the particle number density in both the large and the small mass regimes. For the case in which the masses of the gravitationally produced fermions are small compared to the Hubble expansion rate at the end of inflation, we obtain a universal result for the number density that is nearly independent of the details of the inflationary model. The result is identical to the case of conformally coupled scalars up to an overall multiplicative factor of order unity for reasons other than just counting the fermionic degrees of freedom., Comment: 21 pages, 1 figure

The Standard Model and its extensions predict multiple phase transitions in the early universe. In addition to the electroweak phase transition, one or several of these could occur at energies close to the weak scale. Such phase transitions can leave their imprint on the relic abundance of TeV-scale dark matter. In this paper, we enumerate several physical features of a generic phase transition and parameterize the effect of each on the relic abundance. In particular, we include among these effects the presence of the scalar field vacuum energy and the cosmological constant, which is sensitive to UV physics. Within the context of the Standard Model Higgs sector, we find that the relic abundance of generic TeV-scale dark matter is affected by the vacuum energy at the order of a fraction of a percent. For scalar field sectors with strong first order phase transitions, an order one percent apparent tuning of coupling constants may allow corrections induced by the vacuum energy to be of order unity., Comment: 17 pages, 2 figures

An extension of the MSSM called the munuSSM does not allow a conventional thermal leptogenesis scenario because of the low scale seesaw that it utilizes. Hence, we investigate the possibility of electroweak baryogenesis. Specifically, we identify a parameter region for which the electroweak phase transition is sufficiently strongly first order to realize electroweak baryogenesis. In addition to transitions that are similar to those in the NMSSM, we find a novel class of phase transitions in which there is a rotation in the singlet vector space., Comment: 36 pages, 10 figures

Just as big bang nucleosynthesis allows us to probe the expansion rate when the temperature of the universe was around 1 MeV, the measurement of gravity waves from electroweak scale first order phase transitions may allow us to probe the expansion rate when the temperature of the universe was at the electroweak scale. We compute the simple transformation rule for the gravity wave spectrum under the scaling transformation of the Hubble expansion rate. We then apply this directly to the scenario of quintessence kination domination and show how gravity wave spectra would shift relative to LISA and BBO projected sensitivities., Comment: 28 pages, 2 figures.

We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B-mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super-Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale-dependence and non-Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters., Comment: 107 pages, 14 figures, 17 tables; Inflation Working Group contribution to the CMBPol Mission Concept Study; v2: typos fixed and references added

If inflation is to be considered in an unbiased way, as possibly originating from one of a wide range of underlying theories, then observations need not be simply applied to reconstructing the inflaton potential, V(\phi), or a specific kinetic term, as in DBI inflation, but rather to reconstruct the inflationary action in its entirety. We discuss the constraints that can be placed on a general single field action from measurements of the primordial scalar and tensor fluctuation power spectra and non-Gaussianities. We also present the flow equation formalism for reconstructing a general inflationary Lagrangian, L(X,\phi), with X={1/2}\partial_\mu\phi\partial^\mu\phi, in a general gauge, that reduces to canonical and DBI inflation in the specific gauge \partial L/\partial X = c_s^{-1}., Comment: 16 pages, 1 figure, References added, typos corrected

If the cold dark matter consists of weakly interacting massive particles (WIMPs), anticipated measurements of the WIMP properties at the Large Hadron Collider (LHC) and the International Linear Collider (ILC) will provide an unprecedented experimental probe of cosmology at temperatures of order 1 GeV. It is worth emphasizing that the expected outcome of these tests may or may not be consistent with the picture of standard cosmology. For example, in kination-dominated quintessence models of dark energy, the dark matter relic abundance can be significantly enhanced compared to that obtained from freeze out in a radiation-dominated universe. Collider measurements then will simultaneously probe both dark matter and dark energy. In this article, we investigate the precision to which the LHC and ILC can determine the dark matter and dark energy parameters under those circumstances. We use an illustrative set of four benchmark points in minimal supergravity in analogy with the four LCC benchmark points. The precision achievable together at the LHC and ILC is sufficient to discover kination-dominated quintessence, under the assumption that the WIMPs are the only dark matter component. The LHC and ILC can thus play important roles as alternative probes of both dark matter and dark energy., Comment: 38 pages, 9 figures

Kination dominated quintessence models of dark energy have the intriguing feature that the relic abundance of thermal cold dark matter can be significantly enhanced compared to the predictions from standard cosmology. Previous treatments of such models do not include a realistic embedding of inflationary initial conditions. We remedy this situation by constructing a viable inflationary model in which the inflaton and quintessence field are the same scalar degree of freedom. Kination domination is achieved after inflation through a strong push or "kick" of the inflaton, and sufficient reheating can be achieved depending on model parameters. This allows us to explore both model-dependent and model-independent cosmological predictions of this scenario. We find that measurements of the B-mode CMB polarization can rule out this class of scenarios almost model independently. We also discuss other experimentally accessible signatures for this class of models., Comment: 16 pages, 3 figures

In a companion paper (hep-th/0609150), we have introduced a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a k-essence fluid. In this paper, we study how Cuscuton modifies the constraint sector of Einstein gravity. In particular, we study Cuscuton cosmology and show that even though Cuscuton can have an arbitrary equation of state, or time dependence, and is thus inhomogeneous; its perturbations do not introduce any additional dynamical degree of freedom and only satisfy a constraint equation, amounting to an effective modification of gravity on large scales. Therefore, Cuscuton can be considered to be a minimal theory of evolving dark energy, or a minimal modification of a cosmological constant, as it has no internal dynamics. Moreover, this is the only modification of Einstein gravity to our knowledge that does not introduce any additional degrees freedom (and is not conformally equivalent to the Einstein gravity). We then study two simple Cuscuton models, with quadratic and exponential potentials. The quadratic model has the exact same expansion history as LCDM, and yet contains an early dark energy component with constant energy fraction, which is constrained to < 2%, mainly from WMAP Cosmic Microwave Background (CMB) and SDSS Lyman-alpha forest observations. The exponential model has the same expansion history as the DGP self-accelerating braneworld model, but generates a much smaller Integrated Sachs-Wolfe (ISW) effect, and is thus consistent with the CMB observations. Finally, we show that the evolution is local on super-horizon scales, implying that there is no gross violation of causality, despite Cuscuton's infinite speed of sound., Comment: 10 pages, 5 figures, minor changes and added references, PRD in press

We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a non-canonical kinetic term (or k-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces are the family of Constant Mean Curvature (CMC) hypersurfaces, which are the analogs of soap films (or soap bubbles) in a Euclidian space. This enables us to find the most general solution in 1+1 dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski spacetime, a companion paper (astro-ph/0702002) examines cosmology with Cuscuton dark energy., Comment: 11 pages, 1 figure, added discussion of "coupled cuscuton", matches the published version in PRD

We derive a direct general map from the luminosity distance D(z) to the inhomogeneous matter distribution M(r) in the Lemaitre-Tolman-Bondi (LTB) cosmology and compute several examples. One of our examples explicitly demonstrates that it is possible to tune the LTB cosmological solution to approximately reproduce the luminosity distance curve of a flat FRW universe with a cosmological constant. We also discuss how smooth matter distributions can evolve into naked singularities due to shell crossing when the inhomogeneous ``spatial curvature'' E(r) is a function which changes sign., Comment: 15 pages, 6 figures, RevTeX format

Density perturbations generated from inflation almost always have a spectral index n_s which runs (varies with the wavelength). We explore a running spectral index scenario in which the scalar spectral index runs from blue (n_s >1) on large length scales to red (n_s<1) on short length scales. Specifically, we look for a correlation between the length scale at which n_s-1=0 and the length scale at which tensor to scalar ratio T/S reaches a minimum for single field slow roll inflationary models. By computing the distribution of length scale ratios, we conclude that there indeed is a new approximate consistency condition that is characteristic of running spectral index scenarios that run from blue to red. Specifically, with strong running, we expect 96% of the slow roll models to have the two length scales to be within a factor of 2, with the length scale at which the tensor to scalar ratio reaching a minimum longer than the wavelength at which n_s-1=0., Comment: 18 pages, 2 figures

We discuss constraints on which flat directions can have large vacuum expectation values (VEVs) after inflation. We show that only flat directions which are not charged under B-L and develop positive pressure due to renormalization group effects can have large VEVs of order $\Mp$. For example, within the MSSM only the $H_uH_d$ flat direction is found to be viable. This strongly constrains the embedding of a broad class of inflationary models in the MSSM or some other supersymmetric extension of the SM. For flat directions with negative pressure, the condensate fragments into very large Q-balls which we call Q-giants. We discuss the formation, evolution and reheating of these Q-giants and show that they decay too late. The analysis requires taking into account new phases of the flat directions, which have been overlooked in the formation and dynamics of the Q-balls. These constraints may be ameliorated by invoking a short period of thermal inflation. The latter, however, is viable in a very narrow window of parameter space and requires fine tuning., Comment: 40 pages, 3 figures

Recently, new arguments (astro-ph/0501152, hep-th/0503117) for how corrections from super-Hubble modes can explain the present-day acceleration of the universe have appeared in the literature. However, in this letter, we argue that, to second order in spatial gradients, these corrections only amount to a renormalization of local spatial curvature, and thus cannot account for the negative deceleration. Moreover, cosmological observations already put severe bounds on such corrections, at the level of a few percent, while in the context of inflationary models, these corrections are typically limited to ~ 10^{-5}. Currently there is no general constraint on the possible correction from higher order gradient terms, but we argue that such corrections are even more constrained in the context of inflationary models., Comment: 4 Pages, no figures. Minor modifications, added references

We show that the isocurvature perturbations imply that the gravitationally produced superheavy dark matter must have masses larger than few times the Hubble expansion rate at the end of inflation. This together with the bound on tensor to scalar contribution to the CMB induces a lower bound on the reheating temperature for superheavy dark matter to be about 10^7 GeV. Hence, if the superheavy dark matter scenario is embedded in supergravity models with gravity mediated SUSY breaking, the gravitino bound will squeeze this scenario. Furthermore, the CMB constraint strengthens the statement that gravitationally produced superheavy dark matter scenario prefers a relatively large tensor mode amplitude if the reheating temperature must be less than 10^9 GeV., Comment: 29 pages, 2 figures

The scalar spectral index n is an important parameter describing the nature of primordial density perturbations. Recent data, including that from the WMAP satellite, shows some evidence that the index runs (changes as a function of the scale k at which it is measured) from n>1 (blue) on long scales to n<1 (red) on short scales. We investigate the extent to which inflationary models can accomodate such significant running of n. We present several methods for constructing large classes of potentials which yield a running spectral index. We show that within the slow-roll approximation, the fact that n-1 changes sign from blue to red forces the slope of the potential to reach a minimum at a similar field location. We also briefly survey the running of the index in a wider class of inflationary models, including a subset of those with non-minimial kinetic terms., Comment: 39 pages, 4 figures, references added

We consider a scenario in which our observable universe is a 3-dimensional surface (3-brane) living in extra dimensions with a warped geometry. We show that ``lensed'' density perturbations from other branes serve as possible seeds for structure formation on our observable brane (without inflation), and, in addition, provide constraints on braneworld scenarios with warped bulk geometry. Due to the warped bulk metric, any perturbation generated on one brane (or in the bulk matter) appears to an observer on a second brane to have a significantly different amplitude. We analyze lensed perturbations in the Randall-Sundrum type scenarios and the ``shortcut metric'' scenarios. For Lorentz violating metrics in the bulk, we find the attractive possibility that large density fluctuations that are causally produced elsewhere can lead to small density fluctuations on our brane on superhorizon (acausal) length scales, as required by structure formation. Our most interesting result is that the ``shortcut metrics'' in which geodesics traverse the extra dimensions provide an alternative to inflation with two important features: a possible solution to the horizon problem and a mechanism to generate perturbations necessary for structure formation., Comment: 27 pages

We study a new baryogenesis scenario in a class of braneworld models with low fundamental scale, which typically have difficulty with baryogenesis. The scenario is characterized by its minimal nature: the field content is that of the Standard Model and all interactions consistent with the gauge symmetry are admitted. Baryon number is violated via a dimension-6 proton decay operator, suppressed today by the mechanism of quark-lepton separation in extra dimensions; we assume that this operator was unsuppressed in the early Universe due to a time-dependent quark-lepton separation. The source of CP violation is the CKM matrix, in combination with the dimension-6 operators. We find that almost independently of cosmology, sufficient baryogenesis is nearly impossible in such a scenario if the fundamental scale is above 100 TeV, as required by an unsuppressed neutron-antineutron oscillation operator. The only exception producing sufficient baryon asymmetry is a scenario involving out-of-equilibrium c quarks interacting with equilibrium b quarks., Comment: 39 pages, 5 figures v2: typos, presentational changes, references and acknowledgments added

The phenomenological possibilities of the Randall-Sundrum non-compact extra dimension scenario with the AdS horizon increased to approximately a millimeter length, corresponding to an effective brane tension of TeV^4, are investigated. The corrections to the Newtonian potential are found to be the only observationally accessible probe of this scenario, as previously suggested in the literature. In particular, the presence of the continuum of KK modes does not lead to any observable collider signatures. The extent to which experimental tests of Newtonian gravity can distinguish this scenario from the scenario of Arkani-Hamed, Dimopoulos, and Dvali with one and two millimeter size extra dimensions is explicitly demonstrated., Comment: 22 pages, 2 figures, references added

There is no known fundamental reason to demand as a cosmological initial condition that the bulk possess an SO(3,1) isometry. On the contrary, one expects bulk curvature terms that violate the SO(3,1) isometry at early epochs, leading to a violation of Lorentz invariance on our brane. Demanding that the Lorentz noninvariant terms are small leads to a new ``flatness'' problem, not solved by the usual formulation of inflation. Furthermore, unlike in four dimensions, the Lorentz violations induced from the bulk curvature cannot always be removed as the infrared cutoff is taken arbitrarily large. This means that the equivalence principle in higher dimensions does not guarantee the equivalence principle in dimensionally reduced theories. Near-future experiments are expected to severely constrain these Lorentz-violating ``signatures'' of extra dimensions., Comment: 20 pages, LaTeX

The phenomenon of resonant production of particles {\it after} inflation has received much attention in the past few years. In a new application of resonant production of particles, we consider the effect of a resonance {\em during} inflation. We show that if the inflaton is coupled to a massive particle, resonant production of the particle during inflation modifies the evolution of the inflaton, and may leave an imprint in the form of sharp features in the primordial power spectrum. Precision measurements of microwave background anisotropies and large-scale structure surveys could be sensitive to the features, and probe the spectrum of particles as massive as the Planck scale., Comment: 19 pages, 11 eps figures

We demonstrate a non-inflationary solution to the cosmological horizon problem in scenarios in which our observable universe is confined to three spatial dimensions (a three-brane) embedded in a higher dimensional space. A signal traveling along an extra-dimensional null geodesic may leave our three-brane, travel into the extra dimensions, and subsequently return to a different place on our three-brane in a shorter time than the time a signal confined to our three-brane would take. Hence, these geodesics may connect distant points which would otherwise be ``outside'' the four dimensional horizon (points not in causal contact with one another)., Comment: 9 pages, 2 figures

We consider the cosmology that results if our observable universe is a 3-brane in a higher dimensional universe. In particular, we focus on the case where our 3-brane is located at the $Z_2$ symmetry fixed plane of a $Z_2$ symmetric five-dimensional spacetime, as in the Ho\v{r}ava-Witten model compactified on a Calabi-Yau manifold. As our first result, we find that there can be substantial modifications to the standard Friedmann-Robertson-Walker (FRW) cosmology; as a consequence, a large class of such models is observationally inconsistent. In particular, any relationship between the Hubble constant and the energy density on our brane is possible, including (but not only) FRW. Generically, due to the existence of the bulk and the boundary conditions on the orbifold fixed plane, the relationship is not FRW, and hence cosmological constraints coming from big bang nucleosynthesis, structure formation, and the age of the universe difficult to satisfy. We do wish to point out, however, that some specific choices for the bulk stress-energy tensor components do reproduce normal FRW cosmology on our brane, and we have constructed an explicit example. As our second result, for a broad class of models, we find a somewhat surprising fact: the stabilization of the radius of the extra dimension and hence the four dimensional Planck mass requires unrealistic fine-tuning of the equation of state on our 3-brane. In the last third of the paper, we make remarks about causality and the horizon problem that apply to {\it any} theory in which the volume of the extra dimension determines the four-dimensional gravitational coupling. We point out that some of the assumptions that lead to the usual inflationary requirements are modified., Comment: 15 page REVTeX file; to appear in Phys. Rev. D; clarified the statement of being able to obtain any power dependence of the Hubble expansion rate on the energy density; added references

We show that in large-field inflationary scenarios, superheavy (many orders of magnitude larger than the weak scale) dark matter will be produced in cosmologically interesting quantities if superheavy stable particles exist in the mass spectrum. We show that these particles may be produced naturally during the transition from the inflationary phase to either a matter-dominated or radiation-dominated phase as a result of the expansion of the background spacetime acting on vacuum quantum fluctuations of the dark matter field. We find that as long as there are stable particles whose mass is of the order of the inflaton mass (presumably around $10^{13}$GeV), they will be produced in sufficient abundance to give $\Omega_0 =1$ quite independently of any details of the non-gravitational interactions of the dark-matter field., Comment: 24 page LaTeX file with 2 PostScript figures included with epsf. Error in appendix corrected. No change in conclusions or numerical results