The Nature of Generic Cosmological Singularities

TL;DR

This paper introduces a conformal Hubble-normalized approach to analyze generic cosmological singularities, deriving the cosmological billiard attractor and comparing it with other dynamical systems methods to understand the asymptotic behavior near singularities.

Contribution

It develops a new conformal transformation method that translates spatially homogeneous models into inhomogeneous contexts, enabling the derivation of the cosmological billiard attractor for generic singularities.

Findings

Derivation of the cosmological billiard attractor for generic singularities

Establishment of a duality between different dynamical systems descriptions

Comparison of the conformal approach with metric and Hamiltonian methods

Abstract

The existence of a singularity by definition implies a preferred scale--the affine parameter distance from/to the singularity of a causal geodesic that is used to define it. However, this variable scale is also captured by the expansion along the geodesic, and this can be used to obtain a regularized state space picture by means of a conformal transformation that factors out the expansion. This leads to the conformal `Hubble-normalized' orthonormal frame approach which allows one to translate methods and results concerning spatially homogeneous models into the generic inhomogeneous context, which in turn enables one to derive the dynamical nature of generic cosmological singularities. Here we describe this approach and outline the derivation of the `cosmological billiard attractor,' which describes the generic dynamical asymptotic behavior towards a generic spacelike singularity. We also compare the `dynamical systems picture' resulting from this approach with other work on generic spacelike singularities: the metric approach of Belinskii, Lifschitz, and Khalatnikov, and the recent Iwasawa based Hamiltonian method used by Damour, Henneaux, and Nicolai; in particular we show that the cosmological billiards obtained by the latter and the cosmological billiard attractor form complementary `dual' descriptions of the generic asymptotic dynamics of generic spacelike singularities.