The galileon as a local modification of gravity

TL;DR

This work develops a four-dimensional effective theory for infrared modifications of gravity based on a galileon-like scalar π with derivative self-interactions, demonstrating that a restricted set of Galilean-invariant terms yields second-order equations and enables Vainshtein screening to recover GR locally while permitting self-accelerating backgrounds. It analyzes the coupling to matter, non-linear strong-coupling scales, and the viability of self-accelerating de Sitter solutions, revealing constraints from stability and subluminality, and identifying challenges from retardation and UV completion. The authors further explore symmetry-based routes to a global IR completion, notably via conformal invariance and π as a dilaton, but show that dynamical gravity generically spoils the de Sitter solution on cosmological timescales, complicating a purely four-dimensional UV completion. Overall, the paper clarifies the promise and the hurdles of galileon-like local modifications: they can reproduce observed gravity locally and drive cosmic acceleration without ghosts, yet achieving a consistent, fully UV-complete theory remains an open and subtle endeavor.

Abstract

In the DGP model, the ``self-accelerating'' solution is plagued by a ghost instability, which makes the solution untenable. This fact as well as all interesting departures from GR are fully captured by a four-dimensional effective Lagrangian, valid at distances smaller than the present Hubble scale. The 4D effective theory involves a relativistic scalar π, universally coupled to matter and with peculiar derivative self-interactions. In this paper, we study the connection between self-acceleration and the presence of ghosts for a quite generic class of theories that modify gravity in the infrared. These theories are defined as those that at distances shorter than cosmological, reduce to a certain generalization of the DGP 4D effective theory. We argue that for infrared modifications of GR locally due to a universally coupled scalar, our generalization is the only one that allows for a robust implementation of the Vainshtein effect--the decoupling of the scalar from matter in gravitationally bound systems--necessary to recover agreement with solar system tests. Our generalization involves an internal ``galilean'' invariance, under which π's gradient shifts by a constant. This symmetry constrains the structure of the πLagrangian so much so that in 4D there exist only five terms that can yield sizable non-linearities without introducing ghosts. We show that for such theories in fact there are ``self-accelerating'' deSitter solutions with no ghost-like instabilities. In the presence of compact sources, these solutions can support spherically symmetric, Vainshtein-like non-linear perturbations that are also stable against small fluctuations. [Short version for arxiv]