Vainshtein regime in scalar-tensor gravity: Constraints on degenerate higher-order scalar-tensor theories

Abstract

We study the screening mechanism in the most general scalar-tensor theories that leave gravitational waves unaffected and are thus compatible with recent LIGO/Virgo observations. Using the effective field theory of dark energy approach, we consider the general action for perturbations beyond linear order, focussing on the quasistatic limit. When restricting to the subclass of theories that satisfy the gravitational wave constraints, the fully nonlinear effective Lagrangian contains only three independent parameters. One of these, β 1 , is uniquely present in degenerate higher-order theories. We compute the two gravitational potentials for a spherically symmetric matter source and we find that for β 1 ≥ 0 they decrease as the inverse of the distance, as in standard gravity, while the case β 1 < 0 is ruled out. For β 1 > 0, the two potentials differ and their gravitational constants are not the same on the inside and outside of the body. Generically, the bound on anomalous light bending in the Solar-System constrains β 1 10 −5 . Standard gravity can be recovered outside the body by tuning the parameters of the model, in which case β 1 10 −2 from the Hulse-Taylor pulsar. Theories conformally related to General Relativity admit 0 ≤ β 1 10 −6 , at least for a specific choice of conformal couplings.

Degeneracy, matter coupling, and disformal transformations in scalar-tensor theories

“…The current and main application of DHOST theories is to address cosmic acceleration, however, similar to vanilla scalar-tensor theories, one can consider many noncosmological applications and our analysis will apply there as well. Nonetheless, it is an intriguing question whether our results can potentially complement the existing constraints on such cosmological applications, in particular the recent results on the decay of gravitational waves into dark energy [80], on the destabilization of dark energy inhomogeneities by gravitational waves [81], and on the Vainshtein screening mechanism [32] (see also [31,[82][83][84] and below for other related works). At present these results are quite orthogonal to our work given that the exotic types of matter that we have so far identified as problematic do not play any role in these analyses.…”

“…Although this story is by now well understood, a rather unexplored question concerns the coupling to matter in DHOST. Applications of DHOST coupled to certain matter fields have of course been considered, particularly in the contexts of cosmology and astrophysics (see e.g., [25][26][27][28][29][30][31][32][33]), yet a general understanding of the consistency of matter coupling is currently lacking. This is in fact rather surprising: indeed, besides its obvious relevance for phenomenology, this question is crucial for the claim that the considered theory propagates fewer degrees of freedom than naively expected.…”

Obtaining Precision Constraints on Modified Gravity with Helioseismology

“…This suggests an improvement by more than 2 orders of magnitude on the previous lower (Y > −0.48 [18]) and upper (Y < 0.14 [19]) bounds from astrophysics, and adds to intense previous efforts to constrain Y [18][19][20][48][49][50][51][52][53][54]. The result (7) should be understood within the context of our data-selection criterion, relying on the modes best described by our reference model.…”

Gravitational positivity bounds

“…The bound (5.12) prefers a positive sign of X 2 thoughḠ 2XX < 0 can be allowed due to the non-minimal couplingf 2X even in the shift-symmetric case. See [38,39] for discussions on the screening in the model (5.11).…”