Dynamical systems approach to G2 cosmology

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.

28 pages, 3 tables, 1 *.eps figure, LaTeX2e (10pt), matches version accepted for publication by Classical and Quantum Gravity

References in corpus (3)

• Analytic description of singularities in Gowdy spacetimes
• Manufacture of Gowdy spacetimes with spikes
• G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

Cited by in corpus (32)

• Numerical Approaches to Spacetime Singularities
• The past attractor in inhomogeneous cosmology
• Dynamics of the anisotropic Kantowsky-Sachs geometries in $R^n$ gravity
• Spikes in the Mixmaster regime of G_2 cosmologies
• Dynamics of Brane-World Cosmological Models
• Asymptotic dynamics of the exceptional Bianchi cosmologies
• Spike Oscillations
• New explicit spike solution -- non-local component of the generalized Mixmaster attractor
• Robustness of slow contraction to cosmic initial conditions
• Asymptotic silence-breaking singularities
• Recent developments concerning generic spacelike singularities
• High velocity spikes in Gowdy spacetimes
• Cosmological models from a dynamical systems perspective
• Isotropic singularity in inhomogeneous brane cosmological models
• Gowdy phenomenology in scale-invariant variables
• Spikes and matter inhomogeneities in massless scalar field models
• Asymptotic analysis of spatially inhomogeneous stiff and ultra-stiff cosmologies
• Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background
• The Dynamics of Inhomogeneous Cosmologies
• General relativistic density perturbations
• The fine structure of Gowdy spacetimes
• Non-orthogonally transitive $G_2$ spike solution
• Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
• The Dynamics of Brane-World Cosmological Models
• Cylindrical spikes
• Dynamics and chaos in the unified scalar field cosmology II. System in a finite box
• Full Causal Bulk Viscous Cosmologies with time-varying Constants
• Onset of synchronization in coupled Mixmaster oscillators
• The electromagnetic spike solutions
• Periodic boundary conditions and $G_2$ cosmology
• Mixmaster Fluids Near the Big Bang
• Numerical confirmations of joint spike transitions in $G_2$ cosmologies