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

TL;DR

This paper derives generalized asymptotic solutions for the inflaton field, Hubble parameter, and equation-of-state during the oscillatory reheating phase for potentials near their minima, including quadratic and quartic cases.

Contribution

It provides new explicit asymptotic solutions for the inflaton and related parameters for a range of potentials during reheating, extending previous models.

Findings

Derived asymptotic expansion for quadratic potential.

Explicit solutions for quartic potential using Jacobi elliptic functions.

General implicit solutions involving hypergeometric functions.

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.