Asymptotic analysis of spatially inhomogeneous stiff and ultra-stiff cosmologies

TL;DR

This paper analytically and numerically investigates the decay rates near singularities in inhomogeneous stiff and ultra-stiff cosmologies, confirming and extending the BKL conjectures and isotropization results.

Contribution

It provides new analytical decay rate calculations near singularities for inhomogeneous models with stiff equations of state, supported by numerical simulations.

Findings

Analytical decay rates near singularity for G_0 models.

Numerical validation in G_2 models.

Support for BKL conjectures and isotropization in stiff cosmologies.

Abstract

We calculate analytically the past asymptotic decay rates close to an initial singularity in general G_0 spatially inhomogeneous perfect fluid models with an effective equation of state which is stiff or ultra-stiff (i.e., $\gamma \ge 2$). These results are then supported by numerical simulations in a special class of G_2 cosmological models. Our analysis confirms and extends the BKL conjectures and lends support to recent isotropization results in cosmological models of current interest (with $\gamma > 2$).