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Dynamical systems approach to G2 cosmology

Henk van Elst·Claes Uggla·John Wainwright
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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.

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Henk van Elst, Claes Uggla, John Wainwright. 2001-11-09. Dynamical systems approach to G2 cosmology. https://doi.org/10.1088/0264-9381%2F19%2F1%2F304

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