Acoustics of early universe. II. Lifshitz vs. gauge-invariant theories

TL;DR

This paper compares Lifshitz and gauge-invariant theories of early universe acoustics, reducing complex systems to simpler forms and analyzing metric and density corrections in a radiation-dominated universe.

Contribution

It demonstrates the equivalence of Lifshitz and gauge-invariant approaches and provides exact expressions for metric and density corrections in early universe conditions.

Findings

Lifshitz system reduced to second order differential equation

Equivalence established between Lifshitz and gauge-invariant results

Exact forms of metric and density corrections derived for radiation era

Abstract

Appealing to classical methods of order reduction, we reduce the Lifshitz system to a second order differential equation. We demonstrate its equivalence to well known gauge-invariant results. For a radiation dominated universe we express the metric and density corrections in their exact forms and discuss their acoustic character.