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Techniques are developed to calculate the energy production in quantum fields which obtain a mass through the spontaneous symmetry breaking of a second field which is undergoing a phase transition. All fields are assumed to be out of thermal equilibrium and weakly coupled. The energy produced in a field, which is initially in its ground state, is computed for two generic types of timedependent masses: a roughly monotonic turn on of the mass and an oscillatory mass. The formalism is applied to the questions of particle production and reheating in inflationary universe models. Requirements are found which the couplings in new-inflation-type models must satisfy for efficient reheating to occur.

We study the problem of scalar particle production after inflation by an inflaton field which is oscillating rapidly relative to the expansion of the universe.We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particles produced are described by a quantum scalar field χ, which is coupled to the inflaton via linear and quadratic couplings. The particle production effect is studied using the standard technique of Bogolyubov transformations. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential V (ϕ) = λϕ 4 , the particle production process is very efficient for either type of coupling between the inflaton field and the scalar field χ even for small values of coupling constants. The reheating temperature of the universe in this case is [λ log (1/λ)] −1 times larger than the corresponding estimates based on first order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the scalar field χ and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde and Starobinsky (see e.g. Ref. 13), the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.2

In most current models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, the period of inflation lasts so long that, at the beginning of the inflationary period, the physical wavelengths of comoving scales which correspond to the present large-scale structure of the Universe were smaller than the Planck length. Thus, the usual computations of the spectrum of fluctuations in these models involve extrapolating low energy physics (both in the matter and gravitational sector) into regions where this physics is not applicable. In this article we study the dependence of the usual predictions of inflation for the spectrum of cosmological fluctuations on the hidden assumptions about super-Planck scale physics. We introduce a class of modified dispersion relations to mimic possible effects of super-Planck scale physics, and find that, given an initial state determined by minimizing the energy density, for dispersions relations introduced by Unruh the spectrum is unchanged, whereas for a class of dispersion relations similar to those used by Corley and Jacobson (which involve a more radical departure from the usual linear relation) important deviations from the usual predictions of inflation can be obtained. Some implications of this result for the unification of fundamental physics and early Universe cosmology are discussed.

In pre-big-bang and in ekpyrotic cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting ͑viewed in the Einstein frame͒. The backgrounds studied to date do not yield a scale-invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model ͑neither of pre-big-bang nor of the ekpyrotic form͒ involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar field corresponds to cold matter. We demonstrate that if this contracting phase can be matched via a nonsingular bounce to an expanding Friedmann cosmology, the scale-invariance of the curvature fluctuations is maintained. We also find new background solutions for prebig-bang and for ekpyrotic cosmology, which involve two scalar fields with exponential potentials with background values which are evolving in time. We comment on the difficulty of obtaining a scale-invariant spectrum of adiabatic fluctuations with background solutions which have been studied in the past.

Reheating is an important part of inflationary cosmology. It describes the production of Standard Matter particles after the phase of accelerated expansion. We give a review of the reheating process, focusing on an in-depth discussion of the preheating stage which is characterized by exponential particle production due to a parametric resonance or tachyonic instability. We give a brief overview of the thermalization process after preheating and end with a survey of some applications to supersymmetric theories and to other issues in cosmology such as baryogenesis, dark matter and metric preheating.Comment: Draft of commissioned review article for Annual Reviews of Nuclear and Particle Science, comments welcome! A few references added in this versio

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.