Oscillating 4-Polytopal Universe in Regge Calculus

Abstract

The discretized closed Friedmann-Lemaître-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.

arXiv comment24 pages, 9 figures. arXiv admin note: text overlap with arXiv:1612.06536

References in corpus (7)

• The Hilbert Action in Regge Calculus
• Regge calculus models of closed lattice universes
• Regge calculus models of the closed vacuum $\Lambda$-FLRW universe
• Symplectic and Semiclassical Aspects of the Schläfli Identity
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Expanding Polyhedral Universe in Regge Calculus
• Cosmological modelling with Regge calculus

Cited by in corpus (2)

• Lorentzian quantum cosmology goes simplicial
• Higher Dimensional Polytopal Universe in Regge Calculus