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Nonsingular vacuum cosmologies with a variable cosmological term. (English) Zbl 1045.83065
Summary: We present a class of nonsingular cosmological models with a variable cosmological term described by the second-rank symmetric tensor ${{\Lambda }}_{\mu }^{\nu }$, evolving from ${\Lambda }{\delta }_{\mu }^{\nu }$ to $\lambda {\delta }_{\mu }^{\nu }$ with $\lambda <{\Lambda }$. All ${{\Lambda }}_{\mu }^{\nu }$-dominated cosmologies belong to Lemaître type models for an anisotropic perfect fluid. The expansion starts from a nonsingular non-simultaneous de Sitter bang, with 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 also be 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 ${{\Lambda }}_{\mu }^{\nu }$-dominated cosmologies are Bianchi type I in the planar case and hyperbolic analogues of the Kantowski-Sachs models in the pseudospherical case. At late times all models approach a de Sitter asymptotic with small $\lambda$.
##### MSC:
 83F05 Relativistic cosmology 83C20 Classes of solutions of equations in general relativity 83D05 Relativistic gravitational theories other than Einstein’s