The Gauge issue and the Hamiltonian theory of cosmological perturbations

TL;DR

This paper develops a Hamiltonian formalism for cosmological perturbations, emphasizing gauge-invariant dynamics and spacetime reconstruction, using the Dirac method and Kuchar parametrization for constrained systems.

Contribution

It introduces a comprehensive Hamiltonian framework for cosmological perturbations, refining gauge treatment and spacetime reconstruction techniques.

Findings

Formalism applicable to any homogeneous spacetime

Enhanced understanding of gauge transformations and fixing

Framework facilitates spacetime reconstruction from gauge conditions

Abstract

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. The key element of this approach is the reconstruction of spacetime based on gauge-fixing conditions.