Evolution of Cosmological Perturbations during Reheating
Takashi Hamazaki, Hideo Kodama
TL;DR
This work analyzes the evolution of superhorizon cosmological perturbations during reheating by replacing the oscillating inflaton with a horizon-scale averaged perfect fluid via the WKB approximation and by incorporating energy transfer to radiation. It develops gauge-invariant perturbation equations for a multi-component system, focusing on the Bardeen parameter $\zeta=\Phi-\Upsilon$ and the entropy perturbations $Y$ and $Z$, and derives bounds on entropy growth arising from reheating processes such as parametric resonance and Born decay. The main result is that entropy perturbations generated during reheating are negligibly small, yielding a conserved Bardeen parameter $\Phi-\Upsilon$ on superhorizon scales and validating the standard connection between inflationary fluctuations and post-reheating adiabatic perturbations. This supports the robustness of predicting large-scale structure from inflationary quantum fluctuations, even through realistic reheating dynamics, and highlights the limited role of reheating-induced isocurvature in this framework.
Abstract
The behavior of scalar perturbations on superhorizon scales during the reheating stage is investigated by replacing the rapidly oscillating inflaton field by a perfect fluid obtained by spacetime averaging and the WKB approximation. The influence of the energy transfer from the inflaton to radiation on the evolution of the Bardeen parameter is examined for realistic reheating processes. It is shown that the entropy perturbation generated by the energy transfer is negligibly small, and therefore the Bardeen parameter is conserved in a good accuracy during reheating. This justifies the conventional prescription relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the post-Friedmann stage.