Linear versus nonlinear relaxation: Consequences for reheating and thermalization

We consider the case of a scalar field, the inflaton, coupled to both lighter scalars and fermions, and study the relaxation of the inflaton via particle production in both the linear and nonlinear regimes. This has an immediate application to the reheating problem in inflationary universe models. The linear regime analysis offers a rationale for the standard approach to the reheating problem, but we make a distinction between relaxation and thermalization. We find that particle production when the inflaton starts in the nonlinear region is typically a far more efficient way of transferring energy out of the inflaton zero mode and into the quanta of the lighter scalar than single particle decay. For the nonlinear regime we take into account self-consistently the evolution of the expectation value of the inflaton field coupled to the evolution of the quantum fluctuations. An exhaustive numerical analysis of the renormalized equations reveals that the distribution of produced particles is far from thermal, and exhibits the effect associated with open channels. In the fermionic case, Pauli blocking begins to hinder the transfer of energy into the fermion modes very early on in the evolution of the inflaton. We discuss the issue of thermalization and estimate the reheating temperature to be proportional to the inflaton mass. Cosmological implications are discussed in particular for the Polonyi problem.