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We determine generalised asymptotic solutions for the inflaton field, theHubble parameter, and the equation-of-state parameter valid during theoscillatory phase of reheating for potentials that close to their global minimabehave as even monomial potentials. For the quadratic potential we derive ageneralised asymptotic expansion for the inflaton with respect to the scale setby inverse powers of the cosmic time. For the quartic potential we derive anexplicit, two-term generalised asymptotic solution in terms of Jacobi ellipticfunctions, with a scale set by inverse powers of the square root of the cosmictime. Finally, in the general case, we find similar two-term solutions wherethe leading order term is defined implicitly in terms of the Gauss'hypergeometric function. The relation between the leading terms of theinstantaneous equation-of-state parameter and different averaged values isdiscussed in the general case.

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