Fundamental Cosmic Anisotropy and its Ramifications II: Perturbations in Bianchi spacetimes, and fixed in the Newtonian gauge

TL;DR

This paper develops linear perturbation theory for Bianchi cosmological models, deriving equations in the Newtonian gauge to understand anisotropic universe signatures like CMBs and compare them with standard cosmology.

Contribution

It introduces a general framework for perturbations in Bianchi models, including scalar and tensor modes, and formulates the equations in the Newtonian gauge for arbitrary metrics.

Findings

Derived perturbation equations for density, pressure, momentum, and anisotropic stress.

Formulated the Mukhanov-Sasaki equation for Bianchi models.

Applied results to density contrasts in Einstein-de Sitter and Bianchi I universes.

Abstract

The standard cosmological model is challenged by an ever-growing collection of observations, which invites (and stimulates) inquiry into possible additions and/or alterations. One such alteration comes from letting cosmic isotropy -- as demanded by the cosmological principle -- go, whilst maintaining only homogeneity. This study concerns Bianchi models, a class of anisotropic, homogeneous spacetimes, and in particular their perturbations. Knowledge of their properties under perturbations (such as allowed wavemodes) aids in understanding cosmological signatures of such universes, e.g. CMBs, and thus allows for comparsion to observation and the theory of the standard model. This study develops linear perturbation theory of general Bianchi models, by working in a frame such that metric components depend solely on (cosmic) time. Perturbation equations in the Newtonian gauge, but for arbitrary metric, are derived for energy density $\rho$, (relativistic) pressure $p$, momentum density $q$, and anisotropic stress $\pi$, for the case of scalar and pure tensor perturbations. For the former, the equations for density and pressure are combined to yield the equivalent of the Mukhanov-Sasaki equation for Bianchi models. For a specific choice of metric and fluid flow $u$, the Friedmann equations for Bianchi models are also formulated, as this knowledge is necessary to fully formulate the perturbation equations. Finally, the obtained results are applied to the formulations of density contrasts in an Einstein-de Sitter universe and a Bianchi I universe.