The influence of cosmological transitions on the evolution of density perturbations

TL;DR

This paper resolves debates about how cosmological transitions, particularly reheating and equality, affect superhorizon density perturbations and gravitational waves. It demonstrates the equivalence of gauge-invariant and synchronous formalisms, clarifies the conditions under which the curvature perturbation $\zeta$ is conserved, and re-derives the joining conditions for sharp transitions while confirming their validity under continuous pressure. The authors show that Grishchuk's criticisms of the standard result stem from an incorrect treatment of the smooth reheating transition rather than a failure of the underlying physics, and they recover the conventional amplification of scalar perturbations across transitions. Overall, the work reinforces the standard inflationary predictions for the relative amplitudes of density perturbations and gravitational waves and clarifies how transitions preserve or modify these perturbations in different gauges and transition regimes.

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.