Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 22 (2026), 097, 56 pages      arXiv:2602.03663      https://doi.org/10.3842/SIGMA.2026.097

Dirac Observables for Gowdy Cosmologies Regular at the Big Bang

Max Niedermaier and Mahdi Sedighi Jafari
Department of Physics and Astronomy, University of Pittsburgh, 100 Allen Hall, Pittsburgh, PA 15260, USA

Received February 09, 2026, in final form September 21, 2026; Published online October 14, 2026

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 exact 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.

Key words: two-Killing vector reductions; Lax pair; gravitational observables.

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