Spontaneous compactification of bimetric theory

Abstract

We propose a model of bimetric gravity in which the mixing of metrics naturally provides mass to a graviton by compactification with the flux of two gauge fields in extra dimensions. We assume that each metric in the solution for the background geometry describes four-dimensional Minkowski spacetime with an S2 extra space, though the two radii of S2 for two metrics take on different values in general. The solution is derived by the effective potential method assuming the existence of magnetic fluxes on the extra spheres. We find that a massive graviton is governed by the Fierz–Pauli Lagrangian in the weak field limit and one massless graviton emerges in four-dimensions.