Dynamical systems approach to G2 cosmology

TL;DR

This paper introduces a new dynamical systems approach to analyze spatially inhomogeneous G2 cosmological models, revealing simple geometric descriptions of their behavior near the initial singularity.

Contribution

It develops a scale-invariant, hyperbolic PDE framework for G2 cosmology, enabling detailed analysis of asymptotic behavior near singularities.

Findings

Asymptotic behavior characterized by a local past attractor.

Geometric description of evolution near the initial singularity.

Introduction of a hyperbolic PDE system for cosmological models.

Abstract

In this paper we present a new approach for studying the dynamics of spatially inhomogeneous cosmological models with one spatial degree of freedom. By introducing suitable scale-invariant dependent variables we write the evolution equations of the Einstein field equations as a system of autonomous partial differential equations in first-order symmetric hyperbolic format, whose explicit form depends on the choice of gauge. As a first application, we show that the asymptotic behaviour near the cosmological initial singularity can be given a simple geometrical description in terms of the local past attractor on the boundary of the scale-invariant dynamical state space. The analysis suggests the name ``asymptotic silence'' to describe the evolution of the gravitational field near the cosmological initial singularity.