On the Evolution of Scalar Metric Perturbations in an Inflationary Cosmology

TL;DR

This paper clarifies the amplification process of scalar metric perturbations during inflation, presenting an analytic model of cosmological evolution and addressing recent debates on perturbation behavior during transitions.

Contribution

It introduces a simple analytic inflationary model and confirms the validity of standard results on scalar perturbation amplification through a transition.

Findings

Scalar perturbations are amplified during inflation.

The analytic model illustrates continuous evolution from inflation to radiation era.

Standard results on perturbation amplification are validated.

Abstract

We further clarify how scalar metric perturbations are amplified in an inflationary cosmology. We first construct a simple, analytic model of an inflationary cosmology in which the expansion scale factor evolves continuously from an inflationary era to a radiation-dominated era. From this model, it is clear to see how scalar perturbations are amplified. Second, we examine the recent claims of Grishchuk, and the reply by Deruelle and Mukhanov, regarding the evolution of scalar perturbations through an abrupt transition in the equation of state of the cosmological fluid. We demonstrate that the ``standard results'' regarding the amplification of scalar, density perturbations from inflation are valid.