Massless gravitons on a brane from massive gravity in five-dimensional Minkowski space

TL;DR

This paper demonstrates that by tuning the graviton mass profile in a five-dimensional Minkowski space, one can localize a massless graviton on a brane, effectively reproducing four-dimensional gravity without ghosts or unwanted scalar modes.

Contribution

It introduces a fine-tuned, space-dependent graviton mass profile in five dimensions to localize massless gravitons on a brane, avoiding ghosts and scalar modes, and relates 4D and 5D Planck scales.

Findings

Massless graviton localized with finite mass gap

No ghosts or scalar modes sourced by brane matter

Relation between 4D and 5D Planck masses: M_4^2 = M_5^3 / m_0

Abstract

We discuss the possibility of localizing Einstein gravity on a three-brane embedded in a five-dimensional Minkowski space by giving a space-dependent mass to the graviton. We show that, with an overall fine tuning of the mass profile, it is possible to localize a massless graviton with a finite mass gap from the massive Kaluza-Klein modes. The theory does not contain ghosts and no scalar massless mode is sourced by brane matter. A massless vector mode is strongly coupled to the flux of energy-momentum into the extra dimension, so that it is not sourced as long as only brane-localized matter is considered. In the case where the mass profile has a delta-like shape the four-dimensional Planck mass $M_4$ is related to the five-dimensional one, $M_5$, by $M_4^{2}=M_5^3/m_0$, where $m_0$ is the mass of the first Kaluza-Klein mode of the graviton.