Primordial Perturbation in Horava-Lifshitz Cosmology

Abstract

Recently, Ho\v{r}ava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply the scale invariant primordial perturbation can be generated in any expansion of early universe with a\sim t^n and n>1/3, which, in this note, will be validated by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. However, it is found that it seems that if we require the efolding number of primordial perturbation is suitable for observable universe, n>1 still need to be satisfied, unless the scale of UV regime is quite low.