Primordial perturbation in Hořava-Lifshitz cosmology

Recently, Hořava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply that the scale invariant primordial perturbation can be generated in any expansion of early universe with a∼tn and n>1/3, which, in this Letter, will be confirmed by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. It is found that if enough efolding number of primordial perturbation suitable for observable universe is required, then n≳1 needs to be satisfied, unless the scale of UV regime is quite low. However, the possible UV completeness of HL gravity helps to relax this bound.