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arXiv · 2011.04120

Oscillating 4-Polytopal Universe in Regge Calculus

Ren Tsuda·Takanori Fujiwara
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Abstract

The discretized closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with positive cosmological constant is investigated by Regge calculus. According to the Collins-Williams formalism, a hyperspherical Cauchy surface is replaced with regular 4-polytopes. Numerical solutions to the Regge equations approximate well to the continuum solution during the era of small edge length. Unlike the expanding polyhedral universe in three dimensions, the 4-polytopal universes repeat expansions and contractions. To go beyond the approximation using regular 4-polytopes we introduce pseudo-regular 4-polytopes by averaging the dihedral angles of the tessellated regular 600-cell. The degree of precision of the tessellation is called the frequency. Regge equations for the pseudo-regular 4-polytope have simple and unique expressions for any frequency. In the infinite frequency limit, the pseudo-regular 4-polytope model approaches the continuum FLRW universe.

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Ren Tsuda, Takanori Fujiwara. 2020-11-09. Oscillating 4-Polytopal Universe in Regge Calculus. https://doi.org/10.1093/ptep/ptab079

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