Extended FLRW Models: dynamical cancellation of cosmological anisotropies

TL;DR

This paper studies extended FLRW models with anisotropic Bianchi geometries that expand isotropically, demonstrating that matter and geometrical anisotropies tend to cancel dynamically, leading to asymptotic isotropy and stability under general conditions.

Contribution

It introduces and analyzes the stability of extended FLRW models with anisotropic geometries, showing they are natural attractors in general relativity with matter anisotropies canceling geometrical ones.

Findings

Matter and geometrical anisotropies tend to cancel dynamically.

Extended FLRW models are stable attractors in general relativity.

All shear-free Bianchi type III universes are asymptotically shear-free.

Abstract

We investigate a corner of the Bianchi models that has not received much attention: "extended FLRW models" (eFLRW) defined as a cosmological model with underlying anisotropic Bianchi geometry that nevertheless expands isotropically and can be mapped onto a reference FLRW model with the same expansion history. In order to investigate the stability and naturalness of such models in a dynamical systems context, we consider spatially homogeneous models that contain a massless scalar field $\varphi$ and a non-tilted perfect fluid obeying an equation of state $p=w\rho$. Remarkably, we find that matter anisotropies and geometrical anisotropies tend to cancel out dynamically. Hence, the expansion is asymptotically isotropic under rather general conditions. Although extended FLRW models require a special matter sector with anisotropies that are 'fine-tuned" relative to geometrical anisotropies, our analysis shows that such solutions are dynamically preferred attractors in general relativity. Specifically, we prove that all locally rotationally symmetric Bianchi type III universes with space-like $\nabla_\mu\varphi$ are asymptotically shear-free, for all $w\in[-1,1]$. Moreover, all shear-free equilibrium sets with anisotropic spatial curvature are proved to be stable with respect to all homogeneous perturbations for $w\geq -1/3$.