Nonsingular vacuum cosmologies with a variable cosmological term

TL;DR

This paper introduces nonsingular cosmological models with a variable cosmological term that evolve from an initial nonsingular de Sitter state through anisotropic phases to a late-time de Sitter universe, unifying different symmetry cases.

Contribution

It develops a class of nonsingular cosmologies with a dynamic cosmological tensor, extending previous models to include anisotropic and symmetric cases with detailed evolution analysis.

Findings

Models start from a nonsingular de Sitter bang.

All models approach a late-time de Sitter state.

Different symmetry cases exhibit distinct anisotropic behaviors.

Abstract

We present nonsingular cosmological models with a variable cosmological term described by the second-rank symmetric tensor $\Lambda_{mn}$ evolving from $\Lambda g_{mn}$ to $\lambda g_{mn}$ with $\lambda < \Lambda$. All $\Lambda_{mn}$ dominated cosmologies belong to Lemaitre type models for an anisotropic perfect fluid. The expansion starts from a nonsingular nonsimultaneous de Sitter bang, with $\Lambda$ on the scale responsible for the earliest accelerated expansion, which is followed by an anisotropic Kasner type stage. For a certain class of observers these models can be also identified as Kantowski-Sachs models with regular R regions. For Kantowski-Sachs observers the cosmological evolution starts from horizons with a highly anisotropic ``null bang'' where the volume of the spatial section vanishes. We study in detail the spherically symmetric case and consider the general features of cosmologies with planar and pseudospherical symmetries. Nonsingular $\Lambda_{mn}$ dominated cosmologies are Bianchi type I in the planar case and hyperbolic analogs of the Kantowski-Sachs models in the pseudospherical case. At late times all models approach a de Sitter asymptotic with small $\lambda$.