Scalar-tensor theories and modified gravity in the wake of GW170817

TL;DR

This paper analyzes scalar-tensor theories of gravity in light of GW170817, identifying which theories are consistent with the observed gravitational wave speed and exploring their implications for gravitational laws and screening mechanisms.

Contribution

It characterizes DHOST theories compatible with GW170817 and investigates their screening mechanisms and deviations from standard gravity within matter.

Findings

Identifies DHOST theories with gravitational wave speed equal to light speed.

Derives modified gravitational laws inside matter for these theories.

Provides constraints on theory parameters from astrophysical observations.

Abstract

Theories of dark energy and modified gravity can be strongly constrained by astrophysical or cosmological observations, as illustrated by the recent observation of the gravitational wave event GW170817 and of its electromagnetic counterpart GRB 170817A, which shows that the speed of gravitational waves, $c_g$, is the same as the speed of light, within deviations of order $10^{-15}$. This observation implies very severe restrictions on scalar-tensor theories, in particular theories whose action depends on second derivatives of a scalar field. Working in the very general framework of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, which encompass Horndeski and Beyond Horndeski theories, we present the DHOST theories that satisfy $c_g=c$. We then examine, for these theories, the screening mechanism that suppresses scalar interactions on small scales, namely the Vainshtein mechanism, and compute the corresponding gravitational laws for a non-relativistic spherical body. We show that it can lead to a deviation from standard gravity inside matter, parametrized by three coefficients which satisfy a consistency relation and can be constrained by present and future astrophysical observations.