Cosmological self-tuning and local solutions in generalized Horndeski   theories
  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. 
Eugeny Babichev and Gilles Esposito-Farese
gr-qc