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arXiv · 1609.00806

Waves on accelerating dodecahedral universes

Agnes Bachelot-Motet·Alain Bachelot
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Abstract

We investigate the wave propagation on a compact 3-manifold of constant positive curvature with a non trivial topology, the Poincaré dodecahedral space, when the scale factor is exponentially increasing. We prove the existence of a limit state as t tends to infinity and we get its analytic expression. The deep sky is described by this asymptotic profile thanks to the Sachs-Wolfe formula. We transform the Cauchy problem into a mixed problem posed on a fundamental domain determined by the quaternionic calculus. We perform an accurate scheme of computation: we employ a variational method using a space of second order finite elements that is invariant under the action of the binary icosahedral group.

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Agnes Bachelot-Motet, Alain Bachelot. 2017-02-17. Waves on accelerating dodecahedral universes. https://doi.org/10.1088/1361-6382%2Faa5db8

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