Minimal closed set of observables in the theory of cosmological perturbations. II. Vorticity and gravitational waves.

Abstract

In a previous paper we analyzed the theory of perturbation of Friedmann-Robertson-Walker (FRW) cosmology exclusively in terms of observable quantities in the framework of quasi-Maxwellian equations of gravitation. In that paper we limited ourselves to the case of irrotational perturbations for simplicity. We complete here the previous task by presenting the remaining cases of vector and tensor perturbations. Following the same reasoning as for the scalar case, we show here that the vorticity \ensuremath{\Omega} and the shear \ensuremath{\Sigma} constitute the two basic perturbed variables in terms of which all remaining observable quantities can be described for the vectorial case. The tensorial case can be described by the variables E and H, the electric and magnetic parts of the Weyl conformal tensor. Einstein's equations of general relativity reduce to a closed set of dynamical systems for those pairs of variables. We then obtain a Hamiltonian treatment of the perturbation theory in FRW cosmology.