de Sitterization via Kerr-Schild

TL;DR

This paper introduces a new way to characterize the approach to de Sitter spacetime in cosmological models using Kerr-Schild representations, verified for Kantowski-Sachs models.

Contribution

It proposes a novel characterization of de Sitterization via Kerr-Schild form, demonstrating its effectiveness for certain cosmological models.

Findings

Functions in Kerr-Schild form reveal asymptotic de Sitter behavior.

Verification conducted on Kantowski-Sachs cosmological spacetimes.

The approach offers a new perspective on cosmological evolution toward de Sitter space.

Abstract

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.