Cosmological constraints on Hořava gravity revised in light of GW170817 and GRB170817A and the degeneracy with massive neutrinos

We revise the cosmological bounds on Hořava gravity, taking into account the stringent constraint on the speed of propagation of gravitational waves from GW170817 and GRB170817A. In light of this, we also investigate the degeneracy between massive neutrinos and Hořava gravity. We show that a luminal propagation of gravitational waves suppresses the large-scale cosmic microwave background (CMB) radiation temperature anisotropies, and the presence of massive neutrinos increases this effect. On the contrary, large neutrinos mass can compensate the modifications induced by Hořava gravity in the lensing, matter, and primordial B-mode power spectra. Another degeneracy is found, at a theoretical level, between the tensor-to-scalar ratio r and massive neutrinos, as well as with the model's parameters. We analyze these effects using CMB, supernovae type Ia (SNIa), galaxy clustering, and weak gravitational lensing measurements, and we show how such degeneracies are removed. We find that the model's parameters are constrained to be very close to their general relativity limits, and we get a 2 orders of magnitude improved upper bound, with respect to the big bang nucleosynthesis constraint, on the deviation of the effective gravitational constant from the Newtonian one. The deviance information criterion suggests that in Hořava gravity, Σ m_ν>0 is favored when CMB data only are considered, while the joint analysis of all datasets prefers zero neutrinos mass.