Signature for local Mixmaster dynamics in U(1) symmetric cosmologies

TL;DR

This paper provides evidence that local Mixmaster dynamics characterize the oscillatory approach to singularity in U(1) symmetric, inhomogeneous vacuum cosmologies, with a specific variable serving as a signature of this behavior.

Contribution

It demonstrates that local Mixmaster dynamics are present in U(1) symmetric cosmologies and identifies a variable that signals these oscillations.

Findings

Oscillations in U(1) models match local Mixmaster behavior.

A variable increases at the end of a Mixmaster era, indicating local dynamics.

Supports the view of a local, oscillatory approach to singularity.

Abstract

Previous studies \cite{berger98a} have provided strong support for a local, oscillatory approach to the singularity in U(1) symmetric, spatially inhomogeneous vacuum cosmologies on $T^3 \times R$. The description of a vacuum Bianchi type IX, spatially homogeneous Mixmaster cosmology (on $S^3 \times R$) in terms of the variables used to describe the U(1) symmetric cosmologies indicates that the oscillations in the latter are in fact those of local Mixmaster dynamics. One of the variables of the U(1) symmetric models increases only at the end of a Mixmaster era. Such an increase therefore yields a qualitative signature for local Mixmaster dynamics in spatially inhomogeneous cosmologies.