Isotropic singularity in inhomogeneous brane cosmological models

TL;DR

This paper investigates the nature of the initial singularity in inhomogeneous brane-world cosmological models, finding evidence for an isotropic singularity that could set favorable initial conditions for inflation.

Contribution

It introduces a new dynamical systems approach to analyze inhomogeneous brane cosmologies near the singularity, revealing the generic isotropic nature of the initial singularity.

Findings

Existence of an initial singularity where spatial derivatives are negligible

Initial singularity is isotropic across a range of parameters including radiation and scalar fields

Numerical and qualitative analyses support the isotropic nature of the singularity

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.