Vainshtein Screening in Scalar-Tensor Theories before and after GW170817: Constraints on Theories beyond Horndeski

TL;DR

This paper investigates Vainshtein screening in general scalar-tensor theories, develops an effective perturbation framework, and uses gravitational wave and astrophysical data to constrain these theories beyond Horndeski.

Contribution

It introduces a nonlinear effective approach for cosmological perturbations in scalar-tensor theories and extends previous results on gravitational potential modifications.

Findings

Screening reproduces standard gravity outside and near the body.

Inside the body, gravitational potentials differ, indicating screening breaking.

Observations constrain theory parameters to the order of 0.1 and 0.01.

Abstract

Screening mechanisms are essential features of dark energy models mediating a fifth force on large scales. We study the regime of strong scalar field nonlinearities, known as Vainshtein screening, in the most general scalar-tensor theories propagating a single scalar degree of freedom. We first develop an effective approach to parameterize cosmological perturbations beyond linear order for these theories. In the quasi-static limit, the fully nonlinear effective Lagrangian contains six independent terms, one of which starts at cubic order in perturbations. We compute the two gravitational potentials around a spherical body. Outside and near the body, screening reproduces standard gravity, with a modified gravitational coupling. Inside the body, the two potentials are different and depend on the density profile, signalling the breaking of the Vainshtein screening. We provide the most general expressions for these modifications, revising and extending previous results. We apply our findings to show that the combination of the GW170817 event, the Hulse-Taylor pulsar and stellar structure physics, constrain the parameters of these general theories at the level of $ 10^{-1}$, and of GLPV theories at the level of $10^{-2}$.