Out of equilibrium dynamics of an inflationary phase transition

We study the nonlinear dynamics of an inflationary phase transition in a quartically self-coupled inflaton model within the framework of a de Sitter background. Large $N$ and Hartree nonperturbative approximations combined with nonequilibrium field theory methods are used to study the self-consistent time evolution including back reaction effects. We find that when the system cools down from an initial temperature $T_i>T_c$ to below $T_c$ with the initial value of the zero mode of the inflaton $\phi \mathrm{}\left(0\right)\mathrm{}\ll m{\lambda }^{-1/4}$, the dynamics is determined by the growth of long-wavelength quantum fluctuations. For $\phi \mathrm{}\left(0\right)\mathrm{}\gg m{\lambda }^{-1/4}$ the dynamics is determined by the evolution of the classical zero mode. In the regime where spinodal quantum fluctuations give the most important contribution to the nonequilibrium dynamics, we find that they modify the equation of state providing a graceful exit from the inflationary stage. Inflation ends through this new mechanism at a time scale $t_s>~\left[{H/m}^2\right]\ln \left[{\lambda }^{-1}\right]$ which for $H>~m$ and very weak coupling allows over one hundred $e$-folds during the de Sitter phase. Spatially correlated domains grow to be of horizon size and quantum fluctuations “freeze-out” for times $t>\mathrm{}{t}_s.$