Conformal invariant cosmological perturbations via the covariant approach

TL;DR

This paper revisits the conformal invariance of cosmological perturbations using the covariant approach, clarifying their geometric and physical meanings and simplifying their analysis in alternative gravitational theories.

Contribution

It demonstrates how the covariant approach makes conformal invariant perturbations easily identifiable with clear geometric and physical interpretations.

Findings

Conformal invariant perturbations are easily identified using the covariant approach.

The covariant approach provides clear geometric and physical meanings for perturbation variables.

Simplifies analysis of perturbations in alternative gravitational theories like scalar-tensor theories.

Abstract

It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it is possible to do equivalent analysis in a certain frame in which the perturbation equations are simpler. In this paper we revisit the problem of conformal invariances of cosmological perturbations in terms of the covariant approach in which the perturbation variables have clear geometric and physical meanings. We show that with this approach the conformal invariant perturbations are easily identified.