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Bianchi type I universe with viscous fluid. (English) Zbl 1084.83512
Summary: We study the evolution of a homogeneous, anisotropic Universe given by a Bianchi type-I cosmological model filled with viscous fluid, in the presence of a cosmological constant $\Lambda$. The role of viscous fluid and $\Lambda$ term in the evolution the BI spacetime is studied. Though the viscosity cannot remove the cosmological singularity, it plays a crucial part in the formation of a qualitatively new behavior of the solutions near singularity. It is shown that the introduction of the $\Lambda$ term can be handy in the elimination of the cosmological singularity. In particular, in case of a bulk viscosity, a negative $\Lambda$ provides a never-ending process of evolution, whereas, for some positive values of $\Lambda$ and the bulk viscosity being inverse proportional to the expansion, the BI Universe admits a singularity-free oscillatory mode of expansion. In case of a constant bulk viscosity and share viscosity being proportional to expansion, the model allows both non-periodic and inflationary expansion independent to the sign of $\Lambda$ term.

83C55Macroscopic interaction of the gravitational field with matter (general relativity)
83F05Relativistic cosmology
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