Minimal Closed Set of Observables in the Theory of Cosmological Perturbations

TL;DR

This paper develops a gauge-invariant, observable-based framework for analyzing cosmological perturbations in FRW models, focusing on electric Weyl tensor and shear as fundamental variables, leading to a closed dynamical system.

Contribution

It introduces a minimal set of observable variables, E and Σ, for describing cosmological perturbations, simplifying the analysis and enabling a Hamiltonian formulation.

Findings

E and Σ form a complete basis for perturbations.

Einstein's equations reduce to a closed system for E and Σ.

Framework is gauge-invariant and suitable for Hamiltonian analysis.

Abstract

The theory of perturbation of Friedman-Robertson-Walker (FRW) cosmology is analysed exclusively in terms of observable quantities. Although this can be a very complete and general procedure we limit our presentation here to the case of irrotational perturbations for simplicity. We show that the electric part of Weyl conformal tensor {\bf $E$} and the shear {\bf $\Sigma$} constitute the two basic perturbed variables in terms of which all remaining observable quantities can be described. Einstein\rq s equations of General Relativity reduce to a closed set of dynamical system for {\bf $E$} and {\bf $\Sigma$}. The basis for a gauge-invariant Hamiltonian treatment of the Perturbation Theory in the FRW background is then set up.