Gravity on a Brane in Infinite-Volume Extra Space

TL;DR

This work extends the Dvali-Gabadadze-Porrati framework to branes in infinite-volume extra dimensions with $D>5$, showing that an induced four-dimensional Ricci scalar on a delta-function brane yields Einstein gravity on the brane while the bulk remains infrared-transparent to zero-momentum gravitons. The authors derive the on-brane Newton potential $V(r)=\frac{1}{8\pi \overline M^2 r}$ and demonstrate that the graviton propagator on the brane retains the 4D Einstein tensor structure, with higher-dimensional effects suppressed except for $p^2=0$ modes that can couple to the bulk. They discuss the inverse (infrared) behavior of the bulk, the possibility of solving or softening the cosmological constant problem via bulk-brane dynamics, and implications for hierarchy stabilization through nonperturbative brane-induced scales and large bulk state multiplicities. The paper also analyzes the hierarchy problem and cosmological constant problem within this infinite-volume setup, outlining scenarios in which $M$ can be low yet $\ar M$ is large, and identifying key open questions about flat-brane uniqueness, stability, and realistic cosmologies. Overall, the work proposes a novel gravity-on-brane mechanism with potential implications for fundamental scales and low-energy effective gravity.

Abstract

We generalize the mechanism proposed in [hep-th/0005016] and show that a four-dimensional relativistic tensor theory of gravitation can be obtained on a delta-function brane in flat infinite-volume extra space. In particular, we demonstrate that the induced Ricci scalar gives rise to Einstein's gravity on a delta-function type brane if the number of space-time dimensions is bigger than five. The bulk space exhibits the phenomenon of infrared transparency. That is to say, the bulk can be probed by gravitons with vanishing four-dimensional momentum square, while it is unaccessible to higher modes. This provides an attractive framework for solving the cosmological constant problem.

Figures (1)

• Figure 1: The one-loop diagram which generates the 4D Ricci scalar $\overline R$. Wave lines denote gravitons, solid lines denote massive scalars/fermions. Vertical short lines on scalar/fermion propagators indicate that they are massive.