Brane-World Gravity

TL;DR

This review surveys brane-world gravity, focusing on RS-type 5D warped geometries and low-energy 5D effects that modify 4D gravity through local quadratic and nonlocal Weyl corrections. It develops a covariant brane-world formalism, analyzes gravitational collapse, black holes, and cosmological perturbations, and explores inflation, CMB anisotropies, and gravitational waves within RS and DGP frameworks. It also surveys higher-dimensional extensions (6D) and cascading models, linking phenomenology to holographic ideas and string theory realizations, while highlighting true open problems such as realistic brane-localized black holes and a closed, predictive brane-bulk perturbation theory. Overall, brane-world gravity provides a testbed for M theory-inspired modifications of gravity with potential observational signatures in early-universe cosmology and high-energy astrophysics.

Abstract

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.

Figures (27)

• Figure 1: Schematic of confinement of matter to the brane, while gravity propagates in the bulk (from cav).
• Figure 2: The RS 2-brane model. (Figure taken from cheung.)
• Figure 3: Gravitational field of a small point particle on the brane in RS gauge. (Figure taken from gt.)
• Figure 4: The evolution of the dimensionless shear parameter $\Omega_\mathrm{shear} = \sigma^2/6H^2$ on a Bianchi I brane, for a $V={1\over2}m^2\phi^2$ model. The early and late-time expansion of the universe is isotropic, but the shear dominates during an intermediate anisotropic stage. (Figure taken from mss.)
• Figure 5: The relation between the inflaton mass $m/M_4$ ($M_4\equiv M_\mathrm{p}$) and the brane tension $(\lambda/M_4^4)^{1/4}$ necessary to satisfy the COBE constraints. The straight line is the approximation used in Equation (\ref{['phi55']}), which at high energies is in excellent agreement with the exact solution, evaluated numerically in slow-roll. (Figure taken from mwbh.)