Minimal closed set of observables in the theory of cosmological perturbations

The theory of perturbation of Friedmann-Robertson-Walker (FRW) cosmology is analyzed 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 scalar perturbations for simplicity. That is, we do not consider rotational or gravitational wave contributions to the perturbations. We show that the electric part of the Weyl conformal tensor E and the shear Σ constitute the two basic perturbed variables in terms of which all remaining observable quantities can be described. Einstein’s equations of general relativity reduce to a closed set of dynamical systems for E and Σ. The basis for a gauge-invariant Hamiltonian treatment of the perturbation theory in the FRW background is then set up.