Overall observational constraints on the running parameter λ of Horava-Lifshitz gravity

We use observational data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB), along with requirements of Big Bang Nucleosynthesis (BBN), to constrain the running parameter $\lambda$ of Horava-Lifshitz gravity, which determines the flow between the Ultra-Violet and the Infra-Red. We consider both the detailed and non-detailed balance versions of the gravitational sector, and we include the matter and radiation sectors. Allowing for variation of all the parameters of the theory, we construct the likelihood contours and we conclude that in $1\sigma$ confidence $\lambda$ is restricted to $|\lambda-1|\lesssim0.02$, while its best fit value is $|\lambda_{b.f}-1|\approx0.002$. Although this observational analysis restricts the running parameter $\lambda$ very close to its IR value 1, it does not enlighten the discussion about the theory's possible conceptual and theoretical problems.