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 $w\ge -1/3$.

arXiv comment31 pages, 2 figures; v2: minor amendments to match the version published in CQG

References in corpus (40)

• Planck 2015 results. XIII. Cosmological parameters
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Planck 2013 results. XVI. Cosmological parameters
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Planck evidence for a closed Universe and a possible crisis for cosmology
• Beyond $\Lambda$CDM: Problems, solutions, and the road ahead
• Inflationary Universe with Anisotropic Hair
• CMB Anomalies after Planck
• Large-angle anomalies in the CMB
• Cosmological Limits on Slightly Skew Stresses
• Anisotropic Dark Energy: Dynamics of Background and Perturbations
• Anisotropic Inflation from Vector Impurity
• How Anisotropic is our Universe?
• Cosmology of a Scalar Field Coupled to Matter and an Isotropy-Violating Maxwell Field
• Inflation with stable anisotropic hair: is it cosmologically viable?
• Inflation with Multi-Vector-Hair: The Fate of Anisotropy
• On the Viability of Bianchi Type VIIh Models with Dark Energy
• A dynamical systems approach to the tilted Bianchi models of solvable type
• Does the Isotropy of the CMB Imply a Homogeneous Universe? Some Generalised EGS Theorems
• On the Possibility of Anisotropic Curvature in Cosmology
• The Future of Tilted Bianchi Universes
• On Spacetimes Admitting Shear-free, Irrotational, Geodesic Timelike Congruences
• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies
• Anisotropic cosmologies containing isotropic background radiation
• Anisotropic $2$-form dark energy
• A large scale coherent magnetic field: interactions with free streaming particles and limits from the CMB
• Inflationary Perturbations in Anisotropic, Shear-Free Universes
• Cosmological Signatures of Anisotropic Spatial Curvature
• Anisotropic cosmology and inflation from tilted Bianchi IX model
• Bianchi cosmologies with $p$-form gauge fields
• Bianchi Class B Spacetimes with Electromagnetic Fields
• Tensor Perturbations in Anisotropically Curved Cosmologies
• Balancing Anisotropic Curvature with Gauge Fields in a Class of Shear-Free Cosmological Models
• Shear-free Anisotropic Cosmological Models in f(R) Gravity
• Bianchi models with a free massless scalar field: invariant sets and higher symmetries
• Extending the LCDM model through shear-free anisotropies
• Distance-Redshift Relations in an Anisotropic Cosmological Model
• Dynamically equivalent ΛCDM equations with underlying Bianchi Type geometry

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