Cosmological constraints on Ho\v{r}ava gravity revised in light of
  GW170817 and GRB170817A and the degeneracy with massive neutrinos
  We revise the cosmological bounds on Ho\v{r}ava gravity taking into accounts
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 Ho\v{r}ava 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 Ho\v{r}ava gravity in the
lensing, matter and primordial B-mode power spectra. Another degeneracy is
found, at 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 two 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 Ho\v{r}ava gravity $\Sigma m_\nu>0$ is
favored when CMB data only are considered, while the joint analysis of all
datasets prefers zero neutrinos mass.
