Minimal Closed Set of Observables in the Theory of Cosmological Perturbations

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.