Isotropic cosmological singularities in spatially homogeneous models with a cosmological constant

Abstract

We prove well posedness of the initial value problem for the Einstein equations for spatially homogeneous cosmologies with data at an isotropic cosmological singularity in two cases: for all Bianchi types when the matter content is a cosmological constant with collisionless particles of a single mass (possibly zero), and for FRW, Bianchi-type III, Kantowski–Sachs and Bianchi class A with a cosmological constant and a perfect fluid having the radiation equation of state. In both cases, with a positive cosmological constant, these solutions, except possibly for Bianchi-type IX and Kantowski–Sachs, will expand forever, and be geodesically complete into the future.