  Applying the higher order holonomy corrections to the perturbation theory of
cosmology, the lattice power law of Loop Quantum Cosmology, $\tilde{\mu}\propto
p^{\beta}$, is analysed and the range of $\beta$ is decided to be [-1,0] which
is different from the conventional range $-0.1319>\beta\geq-5/2$ \cite{lqct}.
At the same time, we find that there is a anomaly free condition in this
theory, and we obtain this condition in the vector and tensor mode. We also
find that the nonzero mass of gravitational wave essentially results from the
quantum nature of Riemannian geometry of loop quantum gravity.
