Bianchi spacetimes as super-curvature modes around isotropic cosmologies

TL;DR

This paper demonstrates that certain anisotropic Bianchi models near open Friedmann universes can be interpreted as super-curvature modes, enabling standard perturbation techniques to analyze large-scale anisotropies in cosmology.

Contribution

It provides a detailed identification between anisotropic degrees of freedom in Bianchi models and standard cosmological perturbations, especially super-curvature modes.

Findings

Anisotropic Bianchi models close to open Friedmann spaces correspond to super-curvature perturbations.

Effects of mild anisotropy can be computed using extended standard perturbation techniques.

This approach allows constraining large-scale anisotropies in cosmological observations.

Abstract

A powerful result in theoretical cosmology states that a subset of anisotropic Bianchi models can be seen as the homogeneous limit of (standard) linear cosmological perturbations. Such models are precisely those leading to Friedmann spacetimes in the limit of zero anisotropy. Building on previous works, we give a comprehensive exposition of this result, and perform the detailed identification between anisotropic degrees of freedom and their corresponding scalar, vector, and tensor perturbations of standard perturbation theory. In particular, we find that anisotropic models very close to open (i.e., negatively curved) Friedmann spaces correspond to some type of super-curvature perturbations. As a consequence, provided anisotropy is mild, its effects on all types of cosmological observables can always be computed as simple extensions of the standard techniques used in relativistic perturbation theory around Friedmann models. This fact opens the possibility to consistently constrain, for all cosmological observables, the presence of large scale anisotropies on the top of the stochastic fluctuations.