Cosmic anisotropic doomsday in Bianchi type I universes

Abstract

In order to investigate if the anisotropy of the spacetime may induce future singularities at a finite value of the cosmic time on the evolution of cosmological models, we study vacuum and non-vacuum Bianchi type I spacetimes exhibiting such future singularities. We show that in the case of Kasner vacuum cosmologies the spacetime may rip itself apart in a finite time, and only in the direction corresponding to the unique scale factor which diverges at this finite value of the cosmic time. The other two directional scale factors and the average scale factor do not diverge and tend to zero at this time, while the directional and average expansion rates also become infinite. Due to the absence of the matter content this anisotropic future singularity is induced by the shear scalar, which also blows up at this time. We call such a singularity "Vacuum Rip". For non-vacuum solutions we discuss fully anisotropic Bianchi type I spacetimes filled with a stiff fluid and ellipsoidal (axisymmetric) cosmological models filled with matter with isotropic and anisotropic barotropic pressure, and characterized by $\sigma /\theta =const$, where $\sigma$ and $\theta$ are the shear scalar and the expansion scalar respectively.

10 pages, 6 figures, Accepted for publication in Journal of Mathematical Physics (2016)

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Cited by in corpus (1)

• Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes