Generalised asymptotic solutions for the inflaton in the oscillatory phase of reheating

Abstract

We determine generalised asymptotic solutions for the inflaton field, the Hubble parameter, and the equation-of-state parameter valid during the oscillatory phase of reheating for potentials that close to their global minima behave as even monomial potentials. For the quadratic potential we derive a generalised asymptotic expansion for the inflaton with respect to the scale set by inverse powers of the cosmic time. For the quartic potential we derive an explicit, two-term generalised asymptotic solution in terms of Jacobi elliptic functions, with a scale set by inverse powers of the square root of the cosmic time. Finally, in the general case, we find similar two-term solutions where the leading order term is defined implicitly in terms of the Gauss' hypergeometric function. The relation between the leading terms of the instantaneous equation-of-state parameter and different averaged values is discussed in the general case.