Equation of state and Beginning of Thermalization After Preheating

TL;DR

The paper investigates how the universe transitions from inflation to thermalization by studying the non-equilibrium dynamics of interacting fields during and after preheating.Using fully nonlinear lattice simulations of a chaotic inflation model with g^2 φ^2 χ^2 coupling, it tracks the evolution of the equation of state, occupation numbers, and effective masses.A key finding is that the EOS rapidly becomes radiation-like within ~10^{-35} s, even though the system remains far from full thermal equilibrium, highlighting a pre-thermalized state with turbulent, non-thermal spectra.The work further explores cosmological implications, including the need for three-leg inflaton couplings for complete decay, refinements to the N–log k relation, and the potential for gravitino production and modulated perturbations during prethermalization.

Abstract

We study the out-of-equilibrium nonlinear dynamics of fields after post-inflationary preheating. During preheating, the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out-of-equilibrium inhomogeneous modes, which subsequently evolve towards equilibrium. The infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes. We compute the equation of state during and immediately after preheating. It rapidly evolves towards radiation domination long before the actual thermal equilibrium is established. The exact time of this transition is a non-monotonic function of the coupling between the inflaton and the decay products, and it varies only very weakly (around 10^(-35) s) as this coupling changes over several orders of magnitude. This result is applied to refine the relation between the number of efoldings N and the physical wavelength of perturbations generated during inflation. We also discuss the implications for the theory of modulated perturbations from preheating. We finally argue that many questions of the thermal history of the universe should be addressed in terms of pre-thermalization, illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation. We also highlight the effects of three-legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe.

Figures (13)

• Figure 1: Evolution of the equation of state $w = w(t)$ as a function of time (given in units of $m^{-1}$) for various couplings $g^2$ around $g^2 = 2 \times 10^{-7}$.
• Figure 2: Transition (preheating) time as a function of $g^2$.
• Figure 3: Relative contribution of each of the energy components to the total energy, as a function of time. The vertical axis is the $\log$ of the various energy components in units of the initial energy $m^2\phi_0^2$ multiplied by $a^3$.
• Figure 4: Time evolution of the combination $\omega_{\phi, k} n_k^{\phi}$, for the model $g^2=2.5\cdot 10^{-7}$.
• Figure 5: Same as Fig. \ref{['fig:phinkwk']}, but for the $\chi$ field.