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Peer-reviewedCC BY-SA 4.0Symmetry, Integrability and Geometry: Methods and Applications

Dirac Observables for Gowdy Cosmologies Regular at the Big Bang

  • Max Niedermaier1
  1. 1University of Pittsburgh, USA
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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.

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Cite

BibTeXRIS
BibTeX
@article{niedermaier2026dirac,
  title = {{Dirac Observables for Gowdy Cosmologies Regular at the Big Bang}},
  author = {Max Niedermaier},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications},
  year = {2026},
  month = oct,
  doi = {10.3842/sigma.2026.097},
  url = {https://sigma-journal.com/2026/097/},
  note = {CC BY-SA 4.0},
}
RIS
TY  - JOUR
TI  - Dirac Observables for Gowdy Cosmologies Regular at the Big Bang
AU  - Max Niedermaier
PY  - 2026
DA  - 2026/10/14
JO  - Symmetry, Integrability and Geometry: Methods and Applications
DO  - 10.3842/sigma.2026.097
UR  - https://sigma-journal.com/2026/097/
AB  - 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.
SN  - 1815-0659
ER  -