Brane worlds

TL;DR

This work surveys gravity on codimension-1 branes, detailing the necessary action and boundary terms (including the Gibbons–Hawking term) and the Lanczos–Israel junction conditions that relate bulk geometry to brane energy content. It reviews Newtonian gravity in brane-world scenarios via ADD, RS, and DGP mechanisms, highlighting the crossover scales and resulting potentials that recover four-dimensional gravity at accessible distances. A key result is that standard Friedmann cosmology can be embedded on a 3-brane in the DGP framework when certain integrals over the bulk vanish or match, with explicit examples showing conventional FRW behavior under suitable conditions and potential deviations arising in brane-bulk dynamics and perturbations. The discussion connects these theoretical constructs to phenomenology at short distances and cosmological scales, outlining how brane gravity can mimic or modify four-dimensional gravity depending on the dominant mechanism.

Abstract

This is an introductory review of gravity on branes with an emphasis on codimension 1 models. However, for a new result it is also pointed out that the cosmological evolution of the 3-brane in the model of Dvali, Gabadadze and Porrati may follow the standard Friedmann equation. Contents: 1. Introduction 2. Conventions 3. The Lanczos-Israel matching conditions 4. The action principle with codimension 1 hypersurfaces: Need for the Gibbons-Hawking term 5. The Newtonian limit on thin branes 6. A remark on black holes in the model of Dvali, Gabadadze and Porrati 7. The cosmology of codimension 1 brane worlds