Gauge-fixing and spacetime reconstruction in the Hamiltonian theory of cosmological perturbations

TL;DR

This paper develops a Hamiltonian framework for cosmological perturbations that explicitly handles gauge fixing and spacetime reconstruction, providing a systematic approach applicable to various homogeneous spacetimes.

Contribution

It introduces a refined Hamiltonian method with explicit gauge-fixing and spacetime reconstruction techniques using the Kuchař parametrization, enhancing the analysis of cosmological perturbations.

Findings

Explicit separation of gauge-invariant dynamics from gauge transformations.

Simplified gauge-fixing procedure via a new gauge-fixing space frame.

Application to perturbed Kasner universe with Coulomb-like and Lorenz-like gauges.

Abstract

We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the method via the so-called Kucha\vr parametrization of the kinematical phase space. We separate the gauge-invariant dynamics of the three-surfaces from the three-surface deformations induced by linear coordinate transformations. The canonical group of the three-surface deformations and the complete space of gauge-fixing conditions are explicit in our approach. We introduce a frame in the space of gauge-fixing conditions and use it to considerably simplify the prescription for gauge-fixing, partial gauge-fixing and spacetime reconstruction. Finally, we illustrate our approach by considering the perturbed Kasner universe, for which we discuss two kinds of gauges that correspond respectively to the Coulomb-like and the Lorenz-like gauge in electrodynamics.