On the initial geometry of a vacuum cosmological spacetime

Abstract

In the first part of this paper we consider expanding vacuum cosmological spacetimes with a free $T^N$-action. Among them, we give evidence that Gowdy spacetimes have AVTD (asymptotically velocity term dominated) behavior for their initial geometry, in any dimension. We then give sufficient conditions to reach a similar conclusion about a $T^2$-invariant four dimensional nonGowdy spacetime. In the second part of the paper we consider vacuum cosmological spacetimes with crushing singularities. We introduce a monotonic quantity to characterize Kasner spacetimes. Assuming scale-invariant curvature bounds and local volume bounds, we give results about causal pasts.

final version

References in corpus (3)

• Ancient Dynamics in Bianchi Models: Approach to Periodic Cycles
• Areal Foliation and AVTD Behavior in T^2 Symmetric Spacetimes with Positive Cosmological Constant
• Bianchi VIII and IX vacuum cosmologies: Almost every solution forms particle horizons and converges to the Mixmaster attractor

Cited by in corpus (3)

• Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
• Kasner-like regions near crushing singularities
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant