Generalised Asymptotic Solutions for the Inflaton in the Oscillatory Phase of Reheating

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