Brane-world gravity

TL;DR

This work surveys brane-world gravity, emphasizing 5D warped geometries in which Standard Model fields are confined to a 3+1 dimensional brane while gravity propagates in the bulk. It develops a covariant framework (SMS) to project 5D dynamics onto the brane, revealing local high-energy corrections and nonlocal bulk effects via the Weyl tensor, and analyzes their implications for cosmology, gravitational collapse, and perturbations. Key contributions include detailed treatments of RS1/RS2 geometries, the role of the Weyl “dark radiation” and KK modes, a covariant 1+3 perturbation formalism, and insights into how brane-world corrections modify inflation, gravitational waves, and CMB anisotropies. The findings underscore both the potential observational signatures of higher-dimensional gravity and the need for solving bulk-brane coupling to fully realize predictive brane-world cosmology, with implications for M theory and holography.

Abstract

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+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 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 (~ 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. General relativity cannot describe gravity at high enough energies and must be replaced by a quantum gravity theory, picking up significant corrections as the fundamental energy scale is approached. 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 1+3+d-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting 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 discusses 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.

Figures (13)

• 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 (from cheung).
• Figure 3: Gravitational field of small point particle on the brane in RS gauge (from gt).
• Figure 4: The evolution of the dimensionless shear parameter $\Omega_{\rm shear} = \sigma^2/6H^2$ 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 (from mss).
• Figure 5: The relation between the inflaton mass $m/M_4$ ($M_4\equiv M_{\rm p}$) and the brane tension $(\lambda/M_4^4)^{1/4}$ necessary to satisfy the COBE constraints. The straight line is the approximation used in Eq. (\ref{['phi55']}), which at high energies is in excellent agreement with the exact solution, evaluated numerically in slow-roll. (From mwbh.)