Cosmological self-tuning and local solutions in generalized Horndeski theories

Abstract

We study both the cosmological self-tuning and the local predictions (inside the Solar system) of the most general shift-symmetric beyond Horndeski theory. We first show that the cosmological self-tuning is generic in this class of theories: By adjusting a mass parameter entering the action, a large bare cosmological constant can be effectively reduced to a small observed one. Requiring then that the metric should be close enough to the Schwarzschild solution in the Solar system, to pass the experimental tests of general relativity, and taking into account the renormalization of Newton's constant, we select a subclass of models which presents all desired properties: It is able to screen a big vacuum energy density, while predicting an exact Schwarzschild-de Sitter solution around a static and spherically symmetric source. As a by-product of our study, we identify a general subclass of beyond Horndeski theory for which regular self-tuning black hole solutions exist, in presence of a time-dependent scalar field. We discuss possible future development of the present work.

Black hole solutions in shift-symmetric degenerate higher-order scalar-tensor theories

“…These results agree with those in Ref. [32] which takes G 5 (X) = f 5 (X) = 0, and the particular subclass of the quartic order GLPV theories which provides the self-tuning mechanism of the cosmological constant [30,31].…”

Hairy black holes in DHOST theories: exploring disformal transformation as a solution generating method

“…The well known stealth Schwarzschild solution associated to a constant kinetic term was considered in several works [34][35][36][37][38][39][40][41] and provides the simplest solution for such higher order theories. Conditions on the coupling functions of the DHOST Lagrangian for admitting such stealth black hole solutions have been derived in [42,43].…”

Black holes in self-tuning cubic Horndeski cosmology

“…We also note, following ref. [24], that local gravity tests (such as Solar System tests) are likely to fail for our model if one wants to tune too large a value of the bare cosmological constant. This is true even when non-linear effects, usually responsible for a Vainshtein screening, are taken into account.…”