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

Understand

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.