Analytic and numerical study of preheating dynamics

Abstract

We analyze the phenomenon of preheating, i.e., explosive particle production due to parametric amplification of quantum fluctuations in the unbroken symmetry case, or spinodal instabilities in the broken symmetry phase, using the Minkowski space $\mathrm{O}(N)$ vector model in the large $N$ limit to study the nonperturbative issues involved. We give analytic results for weak couplings and times short compared to the time at which the fluctuations become of the same order as the tree level terms, as well as numerical results including the full back reaction. In the case where the symmetry is unbroken, the analytical results agree spectacularly well with the numerical ones in their common domain of validity. In the broken symmetry case, interesting situations, corresponding to slow roll initial conditions from the unstable minimum at the origin, give rise to a new and unexpected phenomenon: the dynamical relaxation of the vacuum energy. That is, particles are abundantly produced at the expense of the quantum vacuum energy while the zero mode comes back to almost its initial value. In both cases we obtain analytically and numerically the equation of state which in both cases can be written in terms of an effective polytropic index that interpolates between vacuum and radiationlike domination. We find that simplified analyses based on the harmonic behavior of the zero mode, giving rise to a Mathieu equation for the nonzero modes, miss important physics. Furthermore, such analyses that do not include the full back reaction and do not conserve energy result in unbound particle production. Our results rule out the possibility of symmetry restoration by nonequilibrium fluctuations in the cases relevant for new inflationary scenarios. Finally, estimates of the reheating temperature are given, as well as a discussion of the inconsistency of a kinetic approach to thermalization when a nonperturbatively large number of particles are created.