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arXiv · 2105.05325

Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe

Alice Boldrin·Przemysław Małkiewicz
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Abstract

We apply the Dirac procedure for constrained systems to the Arnowitt-Deser-Misner formalism linearized around the Bianchi I universe. We discuss and employ basic concepts such as Dirac observables, Dirac brackets, gauge-fixing conditions, reduced phase space, physical Hamiltonian, canonical isomorphism between different gauge-fixing surfaces and spacetime reconstruction. We relate this approach to the gauge-fixing procedure for non-perturbative canonical relativity. We discuss the issue of propagating a basis for the scalar-vector-tensor decomposition as, in an anisotropic universe, the wavefronts of plane waves undergo a nontrivial evolution. We show that the definition of a gravitational wave as a traceless-transverse mode of the metric perturbation needs to be revised. Moreover there exist coordinate systems in which a polarization mode of the gravitational wave is given entirely in terms of a scalar metric perturbation. We first develop the formalism for the universe with a single scalar field and then extend it to the multi-field case. The obtained fully canonical formalism will serve as a starting point for a complete quantization of the cosmological perturbations and the cosmological background.

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Alice Boldrin, Przemysław Małkiewicz. 2021-05-11. Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe. https://doi.org/10.1088/1361-6382%2Fac3bda

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