Dirac procedure and the Hamiltonian formalism for cosmological perturbations in a Bianchi I universe
arXiv:2105.05325 · doi:10.1088/1361-6382/ac3bda
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.
Added references, corrected typos, clarified notation, improved discussions. Results unchanged
References in corpus (9)
- Theory of cosmological perturbations in an anisotropic universe
- Predictions from an anisotropic inflationary era
- Cosmology without inflation
- Light propagation in a homogeneous and anisotropic universe
- Multiple choices of time in quantum cosmology
- Quantum empty Bianchi I spacetime with internal time
- Dynamics of primordial fields in quantum cosmological spacetimes
- Bianchi type I model with two interacting scalar fields
- Tensor Perturbations in Anisotropically Curved Cosmologies