The cosmological billiard attractor

Abstract

solutions of the Einstein vacuum equations toward a generic spacelike singularity. Starting from fundamental assumptions about the nature of generic spacelike singularities, we derive in a step-by-step manner the cosmological billiard conjecture: we show that the generic asymptotic dynamics of solutions is represented by (randomized) sequences of heteroclinic orbits on the “billiard attractor”. Our analysis rests on two pillars: (i) a dynamical systems formulation based on the conformal Hubblenormalized orthonormal frame approach expressed in an Iwasawa frame; (ii) stochastic methods and the interplay between genericity and stochasticity. Our work generalizes and improves the level of rigor of previous work by Belinskii, Khalatnikov, and Lifshitz; furthermore, we establish that our approach and the Hamiltonian approach to “cosmological billiards”, as elaborated by Damour, Hennaux, and Nicolai, can be viewed as yielding “dual” representations of the asymptotic dynamics.