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arXiv · 2306.01564

Cosmologies with positive Lambda: Hierarchies of future behaviour

Helmut Friedrich
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Abstract

Smooth Cauchy data for the Einstein-Lambda-vacuum field equations with positive cosmological constant Lambda that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary Scri+ in its future. The conformal Einstein equations determine a smooth conformal extension across Scr+ that defines on `the other side' again a Lambda-vacuum solution. In this article we discuss to what extent these properties generalize to the future asymptotic behaviour of solutions to the Einstein-Lambda equations with matter. We study FLRW solutions and the Einstein-Lambda equations coupled to conformally covariant matter transport equations, to conformally privileged matter equations, and to conformally non-covariant matter equations. We present recent results on the Einstein-Lambda-perfect-fluid equations with a non-linear asymptotic dust or asymptotic radiation equation of state.

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Helmut Friedrich. 2023-06-02. Cosmologies with positive Lambda: Hierarchies of future behaviour. https://arxiv.org/abs/2306.01564

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