Cargese Lectures on Brane Induced Gravity

TL;DR

Brane-induced gravity, exemplified by the DGP model, modifies GR by embedding a 4D Einstein term on a brane within a 5D infinite bulk, introducing a crossover scale $m_c$ that governs the transition to 5D gravity. This yields two cosmological branches, conventional and self-accelerated, with distinct cosmology and perturbative limitations; non-linear effects (Vainshtein mechanism) are essential to recover GR near sources, while non-perturbative analyses reveal potential instabilities on the self-accelerated branch due to negative effective 5D mass. The paper also discusses extensions that relax the bulk gravity scale via brane-localized kinetic terms, potentially enabling UV completions and improved embedding. Consequently, brane cosmology exhibits late-time acceleration on the self-accelerated branch and modified Friedmann equations, motivating further model-building to stabilize the self-accelerated sector.

Abstract

A brief introduction is given to the subject of brane induced gravity. The 5D example is discussed in detail. The 4D laws of gravity are obtained on a brane embedded in an infinite volume extra space, where the problem of stabilization of the volume modulus is absent. The theory has two classically disjoint branches of solutions -- the conventional and self-accelerated one. The conventional branch gives a perturbatively stable model of a metastable graviton, with potentially testable predictions within the Solar system. The self-accelerated branch, on the other hand, provides an existence proof for an idea that the accelerated expansion of the Universe could be due to modified gravity. The issue of perturbative stability of the self-accelerated branch is obscured by a breakdown of the conventional perturbative expansion. However, a certain exact non-perturbative solution found in hep-th/0612016 exhibits a net negative gravitational mass, while this mass is positive on the conventional branch. This suggest that the self-accelerated solution must be non-perturbatively unstable. A proposal to overcome this problem in an extension of the original model, that also allows for the quantum gravity scale to be unrestricted, is briefly discussed.