On five-dimensional massive (bi-)gravity

TL;DR

This paper explores five-dimensional massive (bi-)gravity, constructing graviton terms via Cayley-Hamilton theorem and analyzing their effects as effective cosmological constants in various metrics, along with cosmological solutions.

Contribution

It introduces a method to construct higher-dimensional massive graviton terms and examines their cosmological implications in five-dimensional scenarios.

Findings

Massive graviton terms can act as effective cosmological constants.

Constructed graviton terms from Cayley-Hamilton theorem.

Presented cosmological solutions for five-dimensional massive (bi-)gravity.

Abstract

Main results of our recent investigations on five-dimensional scenarios of massive (bi-)gravity will be summarized in this article. In particular, we will show how to construct higher dimensional massive graviton terms from the characteristic equation of square matrix, which is a consequence of the Cayley-Hamilton theorem. Then, we will show whether massive graviton terms of five-dimensional massive (bi-)gravity behave as effective cosmological constants for a number of physical metrics compatible with fiducial ones such as the Friedmann-Lemaitre-Robertson-Walker, Bianchi type I, and Schwarzschild-Tangherlini metrics. Finally, we will show the corresponding cosmological solutions for the five-dimensional massive (bi-)gravity.