Approaches to linear local gauge-invariant observables in inflationary cosmologies

TL;DR

This paper reviews and unifies two recent methods for constructing gauge-invariant observables in inflationary cosmology, providing explicit transformations and establishing their equivalence and completeness.

Contribution

It introduces explicit, covariant, and invertible transformations between two sets of gauge-invariant observables, clarifying their relationship and geometric interpretation.

Findings

Established the equivalence of two gauge-invariant observable constructions.

Provided explicit transformations between the two sets.

Demonstrated the completeness and geometric interpretation of both sets.

Abstract

We review and relate two recent complementary constructions of linear local gauge-invariant observables for cosmological perturbations in generic spatially flat single-field inflationary cosmologies. After briefly discussing their physical significance, we give explicit, covariant and mutually invertible transformations between the two sets of observables, thus resolving any doubts about their equivalence. In this way, we get a geometric interpretation and show the completeness of both sets of observables, while previously each of these properties was available only for one of them.