Isotropic singularity in inhomogeneous brane cosmological models

Abstract

We discuss the asymptotic dynamical evolution of spatially inhomogeneous brane-world cosmological models close to the initial singularity. By introducing suitable scale-invariant dependent variables and a suitable gauge, we write the evolution equations of the spatially inhomogeneous $G_2$ brane cosmological models with one spatial degree of freedom as a system of autonomous first-order partial differential equations. We study the system numerically, and we find that there always exists an initial singularity, which is characterized by the fact that spatial derivatives are dynamically negligible. More importantly, from the numerical analysis we conclude that there is an initial isotropic singularity in all of these spatially inhomogeneous brane cosmologies for a range of parameter values which include the physically important cases of radiation and a scalar field source. The numerical results are supported by a qualitative dynamical analysis and a calculation of the past asymptotic decay rates. Although the analysis is local in nature, the numerics indicates that the singularity is isotropic for all relevant initial conditions. Therefore this analysis, and a preliminary investigation of general inhomogeneous ($G_0$) models, indicates that it is plausible that the initial singularity is isotropic in spatially inhomogeneous brane-world cosmological models and consequently that brane cosmology naturally gives rise to a set of initial data that provide the conditions for inflation to subsequently take place.

32 pages with 8 pictures. submitted to Class. Quant. Grav

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• The Similarity Hypothesis in General Relativity
• Bianchi Cosmologies: A Tale of Two Tilted fluids
• Cosmological models from a dynamical systems perspective
• Large-scale perturbations on the brane and the isotropy of the cosmological singularity
• Asymptotic analysis of spatially inhomogeneous stiff and ultra-stiff cosmologies
• Brane cosmology, Weyl fluid, and density perturbations
• Braneworld Isotropization and Magnetic Fields
• Brane Waves
• The Dynamics of Brane-World Cosmological Models
• Cosmic No Hair for Braneworlds with a Bulk Dilaton Field