论文标题
振荡的4-聚宇宙在regge微积分中
Oscillating 4-Polytopal Universe in Regge Calculus
论文作者
论文摘要
Regge Colculus研究了具有正宇宙常数的离散的封闭的Friedmann-Lema-Robertson-Walker（FLRW）宇宙。根据Collins-Williams的形式主义，超球形的Cauchy表面被常规的4-Polytopes取代。在较小的边缘长度时代，regge方程的数值解决方案与连续溶液的近似值很好。与在三个维度上扩展的多面体宇宙不同，四个聚集体宇宙重复扩张和收缩。为了超越近似值，我们通过平均镶嵌的常规600细胞的二面角来引入伪规范的4-Polytopes。镶嵌的精度称为频率。伪规范4点式的Regge方程对于任何频率都具有简单而独特的表达式。在无限的频率限制中，伪规范的4个polytope模型接近连续性FLRW宇宙。
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.
