Nonequilibrium inflaton dynamics and reheating: Back reaction of parametric particle creation and curved spacetime effects

We present a detailed and systematic analysis of the nonperturbative, nonequilibrium dynamics of a quantum field in the reheating phase of inflationary cosmology, including full back reactions of the quantum field on the curved spacetime, as well as the fluctuations on the mean field. We use the O$\mathrm{}\left(N\right)\mathrm{}$ field theory with unbroken symmetry in a spatially flat Friedmann-Robertson-Walker (FRW) universe to study the dynamics of the inflaton in the post-inflation, preheating stage. Oscillations of the inflaton’s zero mode induce parametric amplification of quantum fluctuations, resulting in a rapid transfer of energy to the inhomogeneous modes of the inflaton field. The large-amplitude oscillations of the mean field, as well as stimulated emission effects require a nonperturbative formulation of the quantum dynamics, while the nonequilibrium evolution requires a statistical field theory treatment. We adopt the coupled nonperturbative equations for the mean field and variance derived in a preceding paper [S. A. Ramsey and B. L. Hu, this issue, Phys. Rev. D 56, 661 (1997)] by means of a two-particle-irreducible (2PI), closed-time-path (CTP) effective action for curved spacetimes while specialized to a dynamical FRW background, up to leading order in the $1/N$ expansion. Adiabatic regularization is employed to yield a covariantly conserved, renormalized energy-momentum tensor. The renormalized dynamical equations are evolved numerically from initial data which are generic to the end state of slow roll in many inflationary cosmological scenarios. The initial conditions consist of a large-amplitude, quasiclassical, oscillating mean field $〈\Phi 〉$ with variance $〈{\Phi }^2〉-〈\Phi {〉}^2$ around the de Sitter-invariant vacuum. We find that for sufficiently large initial mean-field amplitudes $\gtrsim M_P/30\mathrm{}$ (where $M_P$ is the Planck mass) in this model, the parametric resonance effect alone (in a collisionless approximation) is not an efficient means to “preheat” the quantum field. For small initial mean-field amplitude, damping of the mean field via parametric amplification of quantum fluctuations is seen to occur, and in this case can be adequately described by prior analytic studies with approximations based on field theory in Minkowski spacetime. Our results indicate that the self-consistent dynamics of spacetime plays an important role in determining the physics of the post-inflationary Universe. This study calls into question the validity of general claims made without full consideration of the self-consistent dynamics of spacetime and quantum fields.