The influence of cosmological transitions on the evolution of density perturbations

TL;DR

This paper examines how cosmological transitions like reheating and equality affect large-scale density perturbations and gravitational waves, clarifying misconceptions and correcting previous results in inflationary cosmology.

Contribution

It provides a detailed analysis of superhorizon perturbations during cosmological transitions, rectifies recent criticisms, and derives the standard results for smooth reheating transitions.

Findings

Reaffirmation of the conservation law for superhorizon modes.

Correction of previous results regarding smooth reheating transitions.

Demonstration that pressure continuity makes junction conditions less crucial.

Abstract

We study the influence of the reheating and equality transitions on superhorizon density perturbations and gravitational waves. Recent criticisms of the `standard result' for large-scale perturbations in inflationary cosmology are rectified. The claim that the `conservation law' for the amplitude of superhorizon modes was empty is shown to be wrong. For sharp transitions, i.e. the pressure jumps, we rederive the Deruelle-Mukhanov junction conditions. For a smooth transition we correct a result obtained by Grishchuk recently. We show that the junction conditions are not crucial, because the pressure is continuous during the reheating transition. The problem occurred, because the perturbed metric was not evolved correctly through the smooth reheating transition. Finally, we derive the `standard result' within Grishchuks's smooth (reheating) transition.