The Gauge issue and the Hamiltonian theory of cosmological perturbations

Understand

We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime.

• We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological perturbations.
• This approach includes a discussion of the gauge-invariant dynamics of perturbations as well as an analysis of gauge transformations, gauge-fixing, partial gauge-fixing and spacetime reconstruction.
• We will introduce the Kucha\v{r} parametrization of the kinematical phase space as a convenient tool for studying the gauge transformations.