Linearization of homogeneous, nearly-isotropic cosmological models

Abstract

Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann-Robertson-Walker background model. This connects the extensive literature on Bianchi models with the more commonly-adopted perturbation approach to general relativistic cosmological evolution. Expressions for the relevant metric perturbations in familiar coordinate systems can be extracted straightforwardly. Amongst other possibilities, this allows for future analysis of anisotropic matter sources in a more general geometry than usually attempted. We discuss the geometric mechanisms by which maximal symmetry is broken in the context of these models, shedding light on the origin of different Bianchi types. When all relevant length-scales are super-horizon, the simplest Bianchi I models emerge (in which anisotropic quantities appear parallel transported). Finally we highlight the existence of arbitrarily long near-isotropic epochs in models of general Bianchi type (including those without an exact isotropic limit).

31 pages, 2 figures. Submitted to CQG

References in corpus (8)

• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results
• Large-scale BAO signatures of the smallest galaxies
• Bianchi Model CMB Polarization and its Implications for CMB Anomalies
• Markov chain Monte Carlo analysis of Bianchi VII_h models
• Observable effects of anisotropic bubble nucleation
• Rogues' gallery: the full freedom of the Bianchi CMB anomalies
• Temperature and Polarization Patterns in Anisotropic Cosmologies

Cited by in corpus (24)

• How isotropic is the Universe?
• Planck 2013 results. XXVI. Background geometry and topology of the Universe
• Planck 2015 results. XVIII. Background geometry & topology
• Polypolar spherical harmonic decomposition of galaxy correlators in redshift space: Toward testing cosmic rotational symmetry
• Light propagation in inhomogeneous and anisotropic cosmologies
• Weak-lensing by the large scale structure in a spatially anisotropic universe: theory and predictions
• Bayesian analysis of anisotropic cosmologies: Bianchi VII_h and WMAP
• Quantization of Perturbations in an Inflating Elastic Solid
• A framework for testing isotropy with the cosmic microwave background
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Bianchi spacetimes as super-curvature modes around isotropic cosmologies
• Structure formation in an anisotropic universe: Eulerian perturbation theory
• Explicit harmonic and spectral analysis in Bianchi I-VII type cosmologies
• Two-point Correlation Functions in Inhomogeneous and Anisotropic Cosmologies
• Probing the Cosmological Principle with weak lensing shear
• Spatially Homogeneous Universes with Late-Time Anisotropy
• The helical phase of chiral nematic liquid crystals as the Bianchi VII(0) group manifold
• Optimal Boltzmann hierarchies with non-vanishing spatial curvature
• Dynamically equivalent ΛCDM equations with underlying Bianchi Type geometry
• Probing pre-inflationary anisotropy with directional variations in the gravitational wave background
• Spatial anisotropies from long wavelength scalar and tensor modes
• Probing the Cosmological Principle with CMB lensing and cosmic shear
• CMB line-of-sight integrators for nearly-isotropic cosmological models
• Semiclassical Length Measure from a Quantum-Gravity Wave Function