Extended FLRW Models: dynamical cancellation of cosmological anisotropies

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 $\phi$ 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 ${\nabla }_{\mu }\phi$ 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 $w\ge -1/3$.

31 pages, 2 figures; v2: minor amendments to match the version published in CQG

References in corpus (9)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Planck evidence for a closed Universe and a possible crisis for cosmology
• Inflationary Universe with Anisotropic Hair
• Anisotropic Dark Energy: Dynamics of Background and Perturbations
• Anisotropic Inflation from Vector Impurity
• On the Possibility of Anisotropic Curvature in Cosmology
• Inflationary Perturbations in Anisotropic, Shear-Free Universes
• Tensor Perturbations in Anisotropically Curved Cosmologies
• Distance-Redshift Relations in an Anisotropic Cosmological Model

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