Regge calculus models of closed lattice universes

Abstract

This paper examines the behaviour of closed `lattice universes' wherein masses are distributed in a regular lattice on the Cauchy surfaces of closed vacuum universes. Such universes are approximated using a form of Regge calculus originally developed by Collins and Williams to model closed FLRW universes. We consider two types of lattice universes, one where all masses are identical to each other and another where one mass gets perturbed in magnitude. In the unperturbed universe, we consider the possible arrangements of the masses in the Regge Cauchy surfaces and demonstrate that the model will only be stable if each mass lies within some spherical region of convergence. We also briefly discuss the existence of Regge models that are dual to the ones we have considered. We then model a perturbed lattice universe and demonstrate that the model's evolution is well-behaved, with the expansion increasing in magnitude as the perturbation is increased.Comment: 34 pages, 9 figures. Expanded Introduction: elaborated on cosmological context for work and referenced recent work on studying lattice universes using a wide variety of approaches. Corrected an error in the LW graphs in Fig

Towards a cosmological subsector of spin foam quantum gravity

“…In the second part of the article, taking inspiration from a series of works on cosmological modelling with Regge calculus [52][53][54][55][61][62][63][64], we have completed the study of our model by focusing on its classical description. We have first shown that the discretization of spacetime in terms of hyperfrusta have a clear classical interpretation.…”

“…More general settings have been studied on a simplicial discretization of a closed universe. For example, in [61] it has been shown that the Hamiltonian constraint depends on the particle position inside the tetrahedra. In the following analysis we are going to describe the evolution of a single test particle in spacetime.…”

Cosmological solutions with charged black holes

“…The black hole lattice models that we will be considering here have stimulated a good degree of interest over recent years, having been the subject of investigation by a number of different research groups [4][5][6], [7,8], [9][10][11][12], [13][14][15], [16][17][18][19][20][21][22], [23][24][25][26][27], [28][29][30]. Many of these works build on the pioneering studies performed in refs.…”

“…[31] and [32], which provided the Misner initial data for N black holes in asymptotically flat spaces. Some of these approaches have relied on approximation schemes [4][5][6][7][8][9][10][11][12][13][14][15], while others use the methods of numerical relativity [23][24][25][26][27][28][29][30]. Most of them have considered vacuum solutions of Einstein's equations, but some have involved generalisations that include a non-zero cosmological constant [11,14,21,30] and the inclusion of matter modelled as radiation and a scalar field [11,22].…”

Solutions to the reconstruction problem in asymptotic safety

“…1 In this way, we dispense with the need to define a bare actionŜ Λ [ϕ] at the overall cutoff scale Λ and concomitant tuning required to reach the continuum limit. However as emphasised by Manrique and Reuter [26,27] this leaves us with a problem, dubbed by them "the reconstruction problem", 2 since potentially we need access to some bare action to obtain the microscopic degrees of freedom, and from there study possible Hamiltonian formulations, understand more directly properties of the constructed quantum field theory such as constraints and local symmetries, make more direct contact with perturbative approaches, and finally more directly compare this to other approaches that are formulated at the microscopic level, such as canonical quantisation, loop quantum gravity or Monte Carlo simulations [29][30][31][32][33][34][35].…”