Gravitational Leakage into Extra Dimensions: Probing Dark Energy Using Local Gravity

TL;DR

The paper investigates gravity in the DGP braneworld, where the four-dimensional graviton leaks into a five-dimensional bulk at large distances characterized by the crossover scale $r_0$. By solving for the metric of a static spherical source embedded in a de Sitter background, the authors identify two gravitational regimes: an Einstein-like phase near the source and a weak-brane, scalar-tensor phase at larger radii, with a smooth transition governed by $r_0$ and the cosmological expansion. A key result is a universal anomalous precession of up to $5~\mu{\rm as/yr}$ in orbital motion, independent of the source mass and set by the global 5D geometry, along with a lensing behavior that matches GR while Newtonian tests show mass discrepancies that depend on $r_0$ and $R_g$. These findings imply that local, high-precision gravity tests can encode information about the global cosmological framework and the nature of dark energy, offering concrete observational paths in solar-system, cluster, and future space-mission data to probe extra dimensions.

Abstract

The braneworld model of Dvali-Gabadadze-Porrati (DGP) is a theory where gravity is modified at large distances by the arrested leakage of gravitons off our four-dimensional universe. Cosmology in this model has been shown to support both "conventional" and exotic explanations of the dark energy responsible for today's cosmic acceleration. We present new results for the gravitational field of a clustered matter source on the background of an accelerating universe in DGP braneworld gravity, and articulate how these results differ from those of general relativity. In particular, we show that orbits nearby a mass source suffer a universal anomalous precession as large as 5 microarcseconds/year, dependent only on the graviton's effective linewidth and the global geometry of the full, five-dimensional universe. Thus, this theory offers a local gravity correction sensitive to factors that dictate cosmological history.

Figures (1)

• Figure 1: Mass discrepancy, $\delta M$, for a static point source whose Schwarzschild radius is $r_g$. The solid curve is for a self-accelerating background with $H = r_0^{-1}$. The dashed curve is for a FLRW background with $H = r_0^{-1}$.