MINIMAL CLOSED SET OF OBSERVABLES IN THE THEORY OF COSMOLOGICAL PERTURBATIONS .2. VORTICITY AND GRAVITATIONAL-WAVES

In a previous paper we analyzed the theory of perturbation of Friedman n-Robertson-Walker (FRW) cosmology exclusively in terms of observable quantities in the framework of quasi-Maxwellian equations of gravitati on. In that paper we limited ourselves to the case of irrotational per turbations for simplicity. We complete here the previous task by prese nting the remaining cases of vector and tenser perturbations. Followin g the same reasoning as for the scalar case, we show here that the vor ticity Omega and the shear Sigma constitute the two basic perturbed va riables in terms of which all remaining observable quantities can be d escribed for the vectorial case. The tensorial case can be described b y the variables E and H, the electric and magnetic parts of the Weyl c onformal tenser. Einstein's equations of general relativity reduce to a closed set of dynamical systems for those pairs of variables. We the n obtain a Hamiltonian treatment of the perturbation theory in FRW cos mology.