Comment on the "Influence of Cosmological Transitions on the Evolution of Density Perturbations"

TL;DR

This paper critiques a recent claim that the standard inflationary result has been definitively proven, clarifying that the evolution of large-scale density perturbations is unaffected by cosmological transitions, contrary to some interpretations.

Contribution

It demonstrates that the supposed amplification of density perturbations during reheating is a misinterpretation and confirms the invariance of long-wavelength perturbations through cosmological transitions.

Findings

Long-wavelength metric perturbations remain approximately constant during transitions.

Cosmological transitions do not influence the evolution of large-scale perturbations.

The standard inflationary result does not directly follow from the corrected evolution of density perturbations.

Abstract

A recent paper by Martin and Schwarz [1] argues that the ``standard inflationary result" has been finally proven. The result itself is formulated as: ``the closer the inflationary epoch is to the de Sitter space-time, the less important are large-scale gravitational waves in the CMBR today". Beginning from the basic equations of Grishchuk [2, 3] the authors say [1] that Grishchuk's conclusion about approximate equality of metric amplitudes for gravitational waves and density perturbations ``is wrong because the time evolution of the scalar metric perturbation through the (smooth) reheating transition was not calculated correctly". They reiterate a claim about ``big amplification" of scalar perturbations (in contrast to gravitational waves) during reheating. The authors say [1] that after appropriate correction they have recovered the "standard result" within Grishchuk's approach. It is shown in this Comment that the "big amplification" is a misinterpretation. There is no difference in the evolution of long-wavelength metric perturbations for gravitational waves and density perturbations: they both stay approximately constant. The influence of cosmological transitions on the evolution is none at all, as long as the wavelength of the perturbation is much larger than the Hubble radius. It is shown that from the approach of [2, 3] follow the conclusions of [2, 3] without change. Finally, it is argued that the ``standard inflationary result" does not follow from the correct evolution and quantum normalization of density perturbations.