Einstein Gravity on a Brane in 5D Non-compact Flat Spacetime -DGP model revisited-

TL;DR

This paper revisits the DGP 5D gravity model, demonstrating that brane-localized terms can produce 4D Newtonian gravity at long distances without strongly interacting modes, and reproducing Einstein gravity tensor structure.

Contribution

The paper constructs simplified setups with brane-localized derivative terms, showing how 4D gravity emerges in 5D non-compact spacetime and clarifies the graviton tensor structure in DGP models.

Findings

Gravity potential becomes Newtonian at long distances

Bulk gravity coupling can be arbitrarily small

Graviton tensor structure matches 4D Einstein gravity

Abstract

We revisit the 5D gravity model by Dvali, Gabadadze, and Porrati (DGP). Within their framework it was shown that even in 5D non-compact Minkowski space $(x^\mu,z)$, the Newtonian gravity can emerge on a brane at short distances by introducing a brane-localized 4D Einstein-Hilbert term $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$ in the action. Based on this idea, we construct simple setups in which graviton standing waves can arise, and we introduce brane-localized $z$ derivative terms as a correction to $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$. We show that the gravity potential of brane matter becomes $-\frac{1}{r}$ at {\it long} distances, because the brane-localized $z$ derivative terms allow only a smooth graviton wave function near the brane. Since the bulk gravity coupling may be arbitrarily small, strongly interacting modes from the 5D graviton do not appear. We note that the brane metric utilized to construct $\delta(z)M_4^2\sqrt{|\bar{g}_4|}\bar{R}_4$ can be relatively different from the bulk metric by a conformal factor, and show that the graviton tensor structure that the 4D Einstein gravity predicts are reproduced in DGP type models.