  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.
