Spectral expansions of cosmological fields

TL;DR

This paper reviews the theory of cosmological random fields invariant under universe symmetries and introduces new spectral expansion proofs for scalar and spin-weighted fields across different cosmological models.

Contribution

It provides new proofs of spectral expansions for invariant cosmological fields in open, flat, and closed models, advancing the mathematical understanding of these fields.

Findings

Spectral expansions are established for scalar cosmological fields.

Spectral expansions are established for spin-weighted cosmological fields.

Results apply to open, flat, and closed universe models.

Abstract

We give a review of the theory of random fields defined on the observable part of the Universe that satisfy the cosmological principle, i.e., invariant with respect to the 6-dimensional group $\mathcal{G}$ of the isometries of the time slice of the Friedmann--Lema\^{\i}tre--Robertson--Walker standard chart. Our new results include proof of spectral expansions of scalar and spin weighted $\mathcal{G}$-invariant cosmological fields in open, flat, and closed cosmological models.