Inflationary model in minimally modified gravity theories

We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ where, ${\bf H}$ is Hamiltonian constraint Einstein and $p$ constant, has been studied. An inflation difficult to be achieved this unless an additional scalar field playing a role inflaton introduced model. found that with exponential potential can drive graceful exist different case gravity. slow-roll parameter for both power-law potentials inversely proportional number e-folding similar also perturbation curvature comoving gauge on super Hubble radius scales grows rapidly during $p =0$. For tensor modes, amplitude perturbations constant large scales, sound speed diviate unity vary time depending H})$.