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

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2021Department
MatemáticasSource
Universe 2021, 7, 390Abstract
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. 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. Finally, we discuss the physical significance of the generalised
asymptotic solutions in the oscillatory regime and their matching to the appropriate solutions in the
thermalization regime
Subjects
inflationary universe; reheating; asymptotic expansionsCollections
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