Exploring the CMB in Anisotropic Universes

TL;DR

This paper investigates the signatures of anisotropic cosmological models, specifically Bianchi models, on the cosmic microwave background (CMB), challenging the cosmological principle of isotropy.

Contribution

It unifies previous work on anisotropic cosmologies, derives perturbation equations in Bianchi models, and simulates their CMB power spectra to identify potential observational signatures.

Findings

Derived a characteristic PDE for Bianchi models' perturbations

Simulated CMB power spectrum for a Bianchi V model

Provided a framework to test anisotropic cosmologies against observations

Abstract

In recent years, there have been increasing challenges to the cosmological principle, based on new observations of e.g. supernovae and the cosmic bulk flow. As a result, the cosmological community is speaking their concern for the cosmological principle, and from which scales onwards it should apply. In this context, there is a desire to understand more fully the properties and signatures of cosmologies not obeying the cosmological principle. In this article, we let go of the demand of cosmic isotropy, and instead assume only spatial homogeneity in our cosmological models. We follow the results of our previous works [see citations in the list of references], and here bring these together into one unified picture, with the goal of describing the signature(s) of anisotropy in anisotropic cosmological models. We first introduce the Bianchi models -- a particular instance of spatially homogeneous cosmologies -- and show that a metric can be constructed for them when an appropriate collection of desired Killing vector fields is supplied. Then, we give the perturbations of the Friedmann equations in such Bianchi models, in the Newtonian gauge, derived using much the same methodology as applicable to the FLRW models. We show these can be combined into one characteristic partial differential equation. Finally, we use this equation in order to simulate the CMB of a toy Bianchi V example and produce its power spectrum. We close with a discussion, and suggestions for further research.