Cosmological perturbations in the spatially covariant gravity with a dynamical lapse function

We investigate the scalar perturbations in a class of spatially covariant gravity theory with dynamical lapse function. Generally, there are two degrees freedom due to presence velocity treat as analogues those two-field inflationary mode, which one is light mode and other heavy mode. This justified by fact that function becomes infinitely limit when reduces be an auxiliary variable. The standard approaches multiple filed can applied deal our model. By integrating out derive effective for single field, we find solution form plane waves. Then calculate corrections power spectrum from making use perturbative method field theory. At last, fields not weakly coupled, law coupled system large scales.