Spontaneous Compactification of Bimetric Theory

TL;DR

This paper introduces a bimetric gravity model where graviton mass arises naturally from flux compactification of extra dimensions, resulting in one massless and one massive graviton in four-dimensional spacetime.

Contribution

It presents a novel mechanism for graviton mass generation through flux compactification in a bimetric framework, with explicit solutions for the background geometry.

Findings

Massive graviton described by Fierz-Pauli Lagrangian

Existence of a massless graviton in four dimensions

Different radii for extra-dimensional spheres in the solution

Abstract

We propose a model of bimetric gravity in which the mixing of metrics naturally gives a mass to a graviton by the compactification with flux of two gauge fields in extra dimensions. We assume that each metric in the solution for the background geometry describes the four-dimensional Minkowski spacetime with an $S^2$ extra space, though the two radii of $S^2$ for two metrics take different values in general. The solution is derived by the effective potential method in the presence of the magnetic fluxes on the extra spheres. We find that the a massive graviton is governed by the Fierz-Pauli Lagrangian in the weak field limit and one massless graviton left in four dimensions.