Analytic and Numerical Study of Preheating Dynamics

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 $O(N)$ vector model in the large $N$ limit to study the non- perturbative 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 backreaction.In the case where the symmetry is unbroken, the analytic 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 radiation-like domination. We find that simplified analysis based on harmonic behavior of the zero mode, giving rise to a Mathieu equation for the non-zero modes miss important physics. Furthermore analysis that do not include the full backreaction do not conserve energy, resulting in unbound particle production. Our results do not support the recent claim of symmetry restoration by non-equilibrium fluctuations.Finally estimates of the reheating temperature are given,as well as a discussion of the inconsistency of a kinetic approach to thermalization when a non-perturbatively