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arXiv · 2206.06926

Gauge-fixing and spacetime reconstruction in the Hamiltonian theory of cosmological perturbations

Alice Boldrin·Przemysław Małkiewicz
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Abstract

We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the method via the so-called Kucha\vr parametrization of the kinematical phase space. We separate the gauge-invariant dynamics of the three-surfaces from the three-surface deformations induced by linear coordinate transformations. The canonical group of the three-surface deformations and the complete space of gauge-fixing conditions are explicit in our approach. We introduce a frame in the space of gauge-fixing conditions and use it to considerably simplify the prescription for gauge-fixing, partial gauge-fixing and spacetime reconstruction. Finally, we illustrate our approach by considering the perturbed Kasner universe, for which we discuss two kinds of gauges that correspond respectively to the Coulomb-like and the Lorenz-like gauge in electrodynamics.

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Alice Boldrin, Przemysław Małkiewicz. 2022-06-14. Gauge-fixing and spacetime reconstruction in the Hamiltonian theory of cosmological perturbations. https://doi.org/10.1088/1361-6382%2Faca385

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