Discrete Symmetries in Translation Invariant Cosmological Models

TL;DR

This paper explores cosmological models with symmetry properties, analyzing how dimensions expand or contract, and calculates probabilities for different dimensional outcomes up to five dimensions.

Contribution

It introduces a formulation that reveals permutation symmetries in translation-invariant cosmological models and computes dimensional probabilities.

Findings

Probability of dimension expansion or contraction calculated for up to 5 dimensions.

Permutation symmetry effects on cosmological solutions demonstrated.

Framework established for analyzing symmetry effects in higher-dimensional cosmology.

Abstract

In this paper we investigate a class of (d+1) dimensional cosmological models with a cosmological constant possessing an R^d simply transitive symmetry group and show that it can be written in a form that manifests the effect of a permutation symmetry. We investigate the solution orbifold and calculate the probability of a certain number of dimensions that will expand or contract. We use this to calculate the probabilities up to dimension d=5.