Phenomenology of the Gowdy Universe on $T^3 \times R$

TL;DR

This paper investigates the behavior of the Gowdy universe on a three-torus, showing that nonlinear wave equations lead most of the universe to an AVTD regime, with spikes caused by localized absence of nonlinear terms.

Contribution

It demonstrates that nonlinear terms in the wave equations drive the universe toward AVTD behavior, explaining the origin of spiky features at isolated points.

Findings

Most solutions exhibit AVTD behavior near the singularity.

Spiky features are caused by absence of nonlinear terms at specific points.

Numerical evidence supports the conjecture of AVTD dominance.

Abstract

Numerical studies of the plane symmetric, vacuum Gowdy universe on $T^3 \times R$ yield strong support for the conjectured asymptotically velocity term dominated (AVTD) behavior of its evolution toward the singularity except, perhaps, at isolated spatial points. A generic solution is characterized by spiky features and apparent ``discontinuities'' in the wave amplitudes. It is shown that the nonlinear terms in the wave equations drive the system generically to the ``small velocity'' AVTD regime and that the spiky features are caused by the absence of these terms at isolated spatial points.