Evolution of cosmological perturbations in a stage dominated by an oscillatory scalar field

TL;DR

This paper analyzes the evolution of cosmological perturbations during the reheating stage dominated by an oscillating scalar field, demonstrating the constancy of the Bardeen parameter and justifying standard inflationary fluctuation formulas.

Contribution

It shows that despite singularities in the evolution equations, the Bardeen parameter remains nearly constant, validating the use of conventional formulas during reheating.

Findings

Bardeen parameter stays constant during most of reheating.

The behavior of perturbations matches that of a perfect fluid approximation.

Conventional inflationary fluctuation relations are justified during reheating.

Abstract

In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a rapidly oscillating scalar field dominates the energy density, the behavior of perturbations are not known well because their evolution equation expressed in terms of the curvature perturbation becomes singular. In this paper it is shown that in spite of this singular behavior of the evolution equation the Bardeen parameter stays constant in a good accuracy during this stage for superhorizon-scale perturbations except for a sequence of negligibly short intervals around the zero points of the time derivative of the scalar field. This justifies the conventional formula relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the Friedmann stage, except for possible corrections produced by the energy transfer from the scalar field to radiation in the late stage of reheating. It is further shown that outside the above sequence of time intervals the behavior of the perturbations coincides in a good accuracy with that for a perfect fluid system obtained from the original scalar field system by the WKB approximation and a spacetime averaging over a Hubble horizon scale.