On the existence of perturbed robertson-walker universes

Solutions of the full nonlinear field equations of general relativity near the Robertson-Walker universes are examined, together with their relation to linearized perturbations. A method due to Choquet-Bruhat and Deser is used to prove existence theorems for solutions near Robertson-Walker constraint data of the constraint equations on a spacelike hypersurface. These theorems allow one to regard the matter fluctuations as independent quantities, ranging over certain function spaces. In the k = ?1 case the existence theory describes perturbations which may vary within uniform bounds throughout space. When k = +1 a modification of the method leads to a theorem which clarifies some unusual features of these constraint perturbations. The k = 0 existence theorem refers only to perturbations which die away at large distances. The connection between linearized constraint solutions and solutions of the full constraints is discussed. For k = ±1 backgrounds, solutions of the linearized constraints are analyzed using transverse-traceless decompositions of symmetric tensors. Finally the time-evolution of perturbed constraint data and the validity of linearized perturbation theory for Robertson-Walker universes are considered.