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arXiv · 1910.03616

A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories

Marco de Cesare·Edward Wilson-Ewing
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Abstract

We derive transition rules for Kasner exponents in bouncing Bianchi I models with generic perfect fluid matter fields for a broad class of modified gravity theories where cosmological singularities are resolved and replaced by a non-singular bounce. This is a generalization of results obtained previously in limiting curvature mimetic gravity and loop quantum cosmology. A geometric interpretation is provided for the transition rule as a linear map in the Kasner plane. We show that the general evolution of anisotropies in a Bianchi I universe -- including during the bounce phase -- is equivalent to the motion of a point particle on a sphere, where the sphere is the one-point compactification of the Kasner plane. In addition, we study the evolution of anisotropies in a large family of bouncing Bianchi I space-times. We also present a novel explicit solution to the Einstein equations for a Bianchi I universe with ekpyrotic matter with a constant equation of state $ω=3$.

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Marco de Cesare, Edward Wilson-Ewing. 2019-12-10. A generalized Kasner transition for bouncing Bianchi I models in modified gravity theories. https://doi.org/10.1088/1475-7516%2F2019%2F12%2F039

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