Modification of the laws of gravity in the DGP model by the presence of a second DGP brane

TL;DR

This paper explores how adding a second brane in the DGP model modifies gravity laws, revealing a new length scale and potential implications for galaxy rotation curves and black hole physics.

Contribution

It introduces a second brane with localized curvature in the DGP model, deriving a new length scale and analyzing its effects on gravitational potential and particle interactions.

Findings

Discovery of a new length scale as the geometric mean of the DGP scale and brane separation

Weakening of gravitational potential at small distances compared to original DGP

Emergence of a distance-independent force region for 4D observers

Abstract

We investigate how the laws of gravity change in the DGP model, if we add a second, parallel 3-brane, endowed with a localized gravitational curvature term. We calculate the gravitational potential energy between two static point sources localized on different branes. We discover a new length scale, which is equal to the geometric mean of the DGP cross-over scale and the separation of the two branes in the extra dimension. For distances, which are larger than this new length scale, we recover the original DGP result, but for smaller distances the gravitational potential is weaker. Furthermore, a region emerges, where a 4-dimensional observer measures a distance independent force. We discuss a possible application of the present scenario for deriving rotation curves of low surface brightness galaxies. Using the Kaluza-Klein description, we observe a curious pattern, in which even and odd KK-modes contribute to the attractive and repulsive parts of the gravitational potential, respectively. Finally, since this setup allows for the existence of a sector of particle species that are interacting arbitrarily weakly with "our" sector, we discuss the implications of this phenomenon for black holes and the bound on the number of species. We find that the behavior is qualitatively different from theories with a normalizable zero-mode graviton.