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

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 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.

Hamiltonian analysis of higher derivative scalar-tensor theories

“…However, it may seem at odds with the unitary gauge Hamiltonian analysis of [12,14,17], or rather its extrapolation for the quintic terms (as the detailed analysis was in fact restricted to the quartic terms). This apparent paradox is resolved by the fact that some nondegenerate, and thus unhealthy, theories can appear degenerate in the unitary gauge, as discussed in [16]. As the unitary gauge can sometimes be misleading, it is worth revisiting the Hamiltonian analysis of higher derivative theories by considering an arbitrary gauge and check whether we can confirm our conjecture that healthy theories, i.e.…”

“…The coefficients of the quadratic terms in time derivatives have already been computed in [16], and are given by 1…”

“…In a previous paper [16], we reconsidered the question of the Ostrogradski ghost in higher derivative scalar-tensor theories from a different perspective, by focusing on the degeneracy of the Lagrangian. As we showed, the notion of degeneracy is much richer when a variable with secondorder time derivatives is coupled to other degrees of freedom than when it is isolated.…”

Cosmological models in modified gravity theories with extended nonminimal derivative couplings

“…In [16] a new class of scalar-tensor theories was introduced, going beyond Horndeski's theory, where despite the fact that the equations of motion contain higher derivatives, they can be cast in a way that they contain only second-order ones [17]. Additionally, these generalized theories were shown to be free of ghost instabilities in the unitary gauge [18], and later on this was also verified using the Hamiltonian formalism [19][20][21][22][23], due to the existence of a primary constraint which prevents the propagation of extra degrees of freedom [23] (see also [24] and [25][26][27] for additional descriptions).…”

Gravitational scalar–tensor theory

“…This theory is further extended keeping the same number of physical degrees of freedom as standard scalar-tensor theories or the Horndeski's theory while apparent higher derivative terms appear in the action in general [7][8][9][10][11][12] (for further investigations of those theories see also [13][14][15][16][17][18][19][20][21]). Then a natural question will arise : "Can we reformulate those generalized scalar-tensor theories in terms of the metric and its derivatives only, without using a scalar field in the action?…”