An introduction to the Vainshtein mechanism

TL;DR

This paper introduces the Vainshtein mechanism, a nonlinear effect in massive gravity theories that screens extra degrees of freedom at small scales, ensuring consistency with observations and enabling large-scale cosmological effects.

Contribution

It provides a comprehensive, self-contained introduction to the Vainshtein mechanism within various massive gravity models and related theories, clarifying its role and underlying concepts.

Findings

Explains how the Vainshtein mechanism screens extra degrees of freedom.

Connects the mechanism to theories like dRGT and DGP models.

Clarifies the role of nonlinear effects in massive gravity.

Abstract

We introduce the Vainshtein mechanism which plays a crucial role in massive gravities, as well as in related theories such as Galileons and their extensions. This mechanism, also known as k-mouflage, allows to hide via non linear effects - typically for source distances smaller than a so-called Vainshtein radius which depends on the source and on the theory considered - some degrees of freedom whose effects are then only left important at large distances, e.g. for cosmology. It is introduced here in non linear Fierz-Pauli theories (massive gravities), including the dRGT theories, in their decoupling limits, as well as in other models such as DGP model or generalized Galileons. This presentation is self-contained and before discussing the Vainshtein mechanism we introduce some useful results and concepts concerning massive gravity, such as the vDVZ discontinuity, the decoupling limits or the Boulware-Deser ghost.