Application of higher order holonomy corrections to the perturbation theory of cosmology

Applying the higher order holonomy corrections to the perturbation theory of cosmology, the lattice power law of loop quantum cosmology, μ-tilde ∝ pβ, is analyzed and the range of β is decided to be [-1,0] which is different from the conventional range -0.1319 > β ≥ -5/2 (Bojowald M and Hossain G M 2008 Phys. Rev. D 77 023508). At the same time, we find that there is an 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 a gravitational wave essentially results from the quantum nature of the Riemannian geometry of loop quantum gravity.