Large gauge transformations, local coordinates and cosmological observables

TL;DR

This paper discusses new coordinate transformations in cosmology that can alter boundary conditions but shows that cosmological observables remain invariant when all relativistic effects are considered, ensuring consistent model-observation comparisons.

Contribution

It clarifies the invariance of cosmological observable relations under extended coordinate transformations and demonstrates how conformal Fermi coordinates can be globally achieved via standard gauge transformations.

Findings

Cosmological observables are invariant under extended coordinate transformations when all relativistic effects are included.

The ambiguity introduced by new transformations does not affect observable quantities used for model comparison.

Conformal Fermi coordinates can be obtained through a standard gauge transformation, simplifying their implementation.

Abstract

In recent years new types of coordinate transformations have appeared in cosmology on top of the standard gauge transformations, such as the dilatations and special conformal transformations, or the ones leading to (conformal) Fermi coordinates. Some of these can remove effects that are invariant under the standard gauge transformations and also affect asymptotic boundary conditions, thus introducing a non-trivial ambiguity in our cosmological modeling. In this short note we point out that this ambiguity is irrelevant for the quantities we use to compare our model with observations -- the cosmological observable relations -- as they are invariant under all of these transformations. Importantly, this invariance holds only if one takes into account all the relativistic contributions to an observable, which is not the case in the literature in general. We finally also show that the practically-relevant property of conformal Fermi coordinates (a FLRW metric up to second order in distance) can be achieved through a globally-defined standard gauge transformation.