Weak gravity in DGP braneworld model

TL;DR

The work addresses whether four-dimensional GR safely emerges in the DGP braneworld when a bulk cosmological constant and brane tension are included. It introduces a semi-nonlinear perturbation framework with dual gauges to account for general perturbations on a Minkowski brane and analyzes the generalized action, including the bulk AdS curvature scale $\ell$ and crossover scale $r_c$, to derive the brane bending dynamics. The key results show that 4D GR is recovered at short distances $r \lesssim (r_c^2 r_g)^{1/3}$ due to non-linear brane bending, with the leading correction to the Newtonian potential given by $\delta\Phi \sim \sqrt{ \dfrac{r r_g}{2 r_c^2} }$, and that the linear regime exhibits a scale-dependent propagator and tensor structure, consistent with the absence of the vDVZ discontinuity in the $r_c \to \infty$ limit. In the static spherical case, the leading GR correction matches Gruzinov’s result, demonstrating the framework’s accuracy and robustness for weak gravity on the brane.

Abstract

We analyze the weak gravity in the braneworld model proposed by Dvali-Gabadadze-Porrati, in which the unperturbed background spacetime is given by five dimensional Minkowski bulk with a brane which has the induced Einstein Hilbert term. This model has a critical length scale $r_c$. Naively, we expect that the four dimensional general relativity (4D GR) is approximately recovered at the scale below $r_c$. However, the simple linear perturbation does not work in this regime. Only recently the mechanism to recover 4D GR was clarified under the restriction to spherically symmetric configurations, and the leading correction to 4D GR was derived. Here, we develop an alternative formulation which can handle more general perturbations. We also generalize the model by adding bulk cosmological constant and the brane tension.

Figures (1)

• Figure 1: Summary of the results of linear analysis, which is valid when $r\gg (r_c^2 r_g)^{1/3}$. The horizontal axis represents length scale. The raws labeled ${\cal D}$ and $\alpha$, respectively, explain the property of the propagator ${\cal D}$ and the indicator of the tensor structure $\alpha$.