de Sitterization via Kerr-Schild

Spatially homogeneous cosmological spacetimes, evolving in the presence of a positive cosmological constant and matter satisfying some reasonable energy conditions, typically approach the de Sitter geometry asymptotically (at least locally). In this work, we propose an alternate way to characterize this phenomena. We focus on a subset of such models admitting a generalized Kerr-Schild representation. We argue that the functions which define such a representation can be chosen, such that, their asymptotic behavior make the evolution towards the de Sitter spacetime manifest through the representation. We verify our claim for the Kantowski-Sachs family of cosmological spacetimes.