Classical and Quantum Cosmology of Multigravity

TL;DR

This paper extends multigravity theories from simple to general graphs, explores classical and quantum cosmological solutions, and finds oscillating scale factors indicating repeated acceleration and deceleration.

Contribution

It generalizes multigravity models to arbitrary graphs and develops a nonlinear vierbein formalism for cosmological analysis.

Findings

Scale factors exhibit oscillating acceleration and deceleration.

Modes of particles depend on the underlying graph structure.

The theory includes classical and quantum cosmological solutions.

Abstract

Recently, a multigraviton theory on a simple closed circuit graph corresponding to the discretization of $S^1$ compactification of the Kaluza-Klein (KK) theory has been considered. In the present paper, we extend this theory to that on a general graph and study what modes of particles are included. Furthermore, we generalize it in a possible nonlinear theory based on the vierbein formalism and study classical and quantum cosmological solutions in the theory. We found that scale factors in a solution for this theory repeat acceleration and deceleration.