Complete sets of functions for perturbations of Robertson Walker cosmologies
Journal of Mathematical Physics
Crucial to a knowledge of the perturbations of Robertson Walker cosmological models is a knowledge of complete sets of functions with which to expand such perturbations. For the open Robertson Walker cosmology, this question will be completely answered. In addition, some observations will be made concerning explicit solution by separation of variables of wave equations for spin s in a Riemannan space having an infinitesmal line element of which the Robertson Walker models are a special case. I.
... a special case. I. VECTOR AND TENSOR HARMONICS ON THREE-DIMENSIONAL SPACES OF CONSTANT RIEMANNIAN CURVATURE The original investigations of Lifshitz' and Lifshitz and Khalatnikov' into the gravitational stability of the Robertson Walker (RW) isotropic cosmological models" demonstrated the utility of scalar, vector, and tensor harmonics in giving a complete description of small perturbations. In particular these authors"' showed that in the synchronous gauge all perturbations involving pressure, density, velocity, and metric fluctuations can be obtained once a complete set ofsuch functions is found for S, (three-dimensional sphere), 1415