Large gauge transformations, local coordinates and cosmological observables. (3rd November 2022)

• Record Type: Journal Article
• Authors: Mitsou, Ermis; Yoo, Jaiyul
• Is Part Of: Classical and quantum gravity. Volume 39:Number 21(2022)
• Publication Date: 2022-11-03
• Subjects: cosmological observables -- Fermi coordinates -- large gauge transformations; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/1361-6382/ac9724
• Languages: English
• ISSNs: 0264-9381

Abstract

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 Friedmann-Lemaître-Robertson-Walker (FLRW) metric up to second order in distance) can be achieved through a globally-defined standard gauge transformation.