Inhomogeneous post-inflationary Lambda-CDM cosmology as a moduli space expansion

Abstract

We model the large scale late time universe as a Lambda-CDM cosmology driven by cosmological constant and perfect dust fluid. Our aim is to find new solutions in the matter and Lambda epoch consistent with inflationary initial conditions, namely that to the far past in the matter era the cosmology tends to a flat FLRW solution. We identify the moduli degrees of freedom that parametrize the flat Lambda-dust FLRW solution and then promote these moduli to slowly varying functions of the spatial coordinates and show how to solve the Einstein equations in a comoving gradient expansion, controlled by the cosmological constant length scale. Our initial conditions ensure that the approximation remains under control to the far past of the matter era, and to the far future of Lambda domination. The solution is fully non-perturbative in the amplitude of the metric deformation, and we explicitly construct it to fourth order in derivatives. A general Lambda-dust universe dominated by Lambda in the future is characterized by a 3-metric and a stress tensor (with positive trace) defined on the future conformal boundary. The new cosmologies with inflationary initial conditions are characterized only by the boundary 3-metric, the stress tensor being locally determined entirely in terms of that metric.