Dirac Observables for Gowdy Cosmologies regular at the Big Bang

TL;DR

This paper constructs a comprehensive set of Dirac observables for Gowdy cosmologies, demonstrating their regularity at the Big Bang and linking them to simpler Carroll-type gravity observables, thereby extending the understanding of early universe dynamics.

Contribution

It introduces an infinite set of Dirac observables for Gowdy cosmologies that are valid off-shell and regular at the Big Bang, connecting them to Carroll gravity theory.

Findings

Dirac observables remain regular at the Big Bang.

Matching of Gowdy observables with Carroll gravity observables.

Systematic anti-Newtonian expansion of observables.

Abstract

Gowdy cosmologies are exact, spatially inhomogeneous solutions of the vacuum Einstein equations which describe nonlinear gravitational waves coalescing at the Big Bang singularity. With toroidal spatial sections they provenly have the Asymptotic Velocity Domination property, in that close to the Big Bang dynamical spatial gradients fade out and the dynamics is governed by a Carroll-type gravity theory. Here we construct an infinite set of Dirac observables for Gowdy cosmologies, valid off-shell, strongly, and without gauge fixing. These observables stay regular at the Big Bang and can be matched to much simpler Dirac observables of the Carroll-type gravity theory. Conversely, in an adapted foliation there is a systematic anti-Newtonian expansion (in inverse powers of the reduced Newton constant) of the full Dirac observables whose leading terms are the Carroll ones. In particular, this provides an off-shell generalization of the Asymptotic Velocity Domination property.