Brane world corrections to Newton's law

TL;DR

This paper reviews how various brane world models predict modifications to Newton's law of gravity at small and large scales, with implications for astrophysics and cosmology.

Contribution

It provides a comprehensive review of corrections to Newton's law in diverse brane world scenarios, including models with different dimensions and configurations.

Findings

Corrections to Newton's law occur at small radii near the bulk length scale.

Gravity becomes effectively multidimensional at small scales in these models.

Superlight modes can alter gravity at large scales, impacting cosmology.

Abstract

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After a brief general exposition, we review in more detail the predicted corrections to Newton's law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein-Gauss-Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton's law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.