Massive Gravity on a Brane

TL;DR

This work analyzes a warped two-brane model with brane-localized Fierz–Pauli mass terms to realize massive gravity on large scales while preserving UV Einstein gravity. Using linearized 5D gravity, boundary conditions, and a detailed two-point function calculation on the Planck brane, the authors show that the low-energy spectrum contains a massive spin-2 state plus a radion that becomes a ghost when the IR mass term is active, signaling a fundamental inconsistency. They derive the UV-brane massive-gravity behavior with $m^2 = 2\lambda_{UV}/R$ and find a vDVZ-like discontinuity, along with a finite-width decay of the would-be massive graviton into KK states in certain limits, indicating instability as the IR sector decouples. Collectively, the results highlight substantial challenges—ghost radion and non-Einstein propagator structures—in constructing a fully consistent brane realization of massive gravity, while providing a concrete framework for assessing holographic and boundary-condition effects on 4D gravity.

Abstract

At present no theory of a massive graviton is known that is consistent with experiments at both long and short distances. The problem is that consistency with long distance experiments requires the graviton mass to be very small. Such a small graviton mass however implies an ultraviolet cutoff for the theory at length scales far larger than the millimeter scale at which gravity has already been measured. In this paper we attempt to construct a model which avoids this problem. We consider a brane world setup in warped AdS spacetime and we investigate the consequences of writing a mass term for the graviton on a the infrared brane where the local cutoff is of order a large (galactic) distance scale. The advantage of this setup is that the low cutoff for physics on the infrared brane does not significantly affect the predictivity of the theory for observers localized on the ultraviolet brane. For such observers the predictions of this theory agree with general relativity at distances smaller than the infrared scale but go over to those of a theory of massive gravity at longer distances. A careful analysis of the graviton two-point function, however, reveals the presence of a ghost in the low energy spectrum. A mode decomposition of the higher dimensional theory reveals that the ghost corresponds to the radion field. We also investigate the theory with a brane localized mass for the graviton on the ultraviolet brane, and show that the physics of this case is similar to that of a conventional four dimensional theory with a massive graviton, but with one important difference: when the infrared brane decouples and the would-be massive graviton gets heavier than the regular Kaluza--Klein modes, it becomes unstable and it has a finite width to decay off the brane into the continuum of Kaluza-Klein states.