Horava Gravity in the Effective Field Theory formalism: from cosmology
  to observational constraints
  We consider Horava gravity within the framework of the effective field theory
(EFT) of dark energy and modified gravity. We work out a complete mapping of
the theory into the EFT language for an action including all the operators
which are relevant for linear perturbations with up to sixth order spatial
derivatives. We then employ an updated version of the EFTCAMB/EFTCosmoMC
package to study the cosmology of the low-energy limit of Horava gravity and
place constraints on its parameters using several cosmological data sets. In
particular we use cosmic microwave background (CMB) temperature-temperature and
lensing power spectra by Planck 2013, WMAP low-l polarization spectra, WiggleZ
galaxy power spectrum, local Hubble measurements, Supernovae data from SNLS,
SDSS and HST and the baryon acoustic oscillations measurements from BOSS, SDSS
and 6dFGS. We get improved upper bounds, with respect to those from Big Bang
Nucleosynthesis, on the deviation of the cosmological gravitational constant
from the local Newtonian one. At the level of the background phenomenology, we
find a relevant rescaling of the Hubble rate at all epoch, which has a strong
impact on the cosmological observables; at the level of perturbations, we
discuss in details all the relevant effects on the observables and find that in
general the quasi-static approximation is not safe to describe the evolution of
perturbations. Overall we find that the effects of the modifications induced by
the low-energy Horava gravity action are quite dramatic and current data place
tight bounds on the theory parameters.
