Adiabatic and non-adiabatic perturbations for loop quantum cosmology

We generalize the perturbations theory of loop quantum cosmology to a hydrodynamical form and define an effective curvature perturbation on an uniform density hypersurfaces $\zeta_e$. As in the classical cosmology, $\zeta_e$ should be gauge-invariant and conservation on the large scales. The evolutions of both the adiabatic and the non-adiabatic perturbations for a multi-fluids model are investigated in the framework of the effective hydrodynamical theory of loop quantum cosmology with the inverse triad correction. We find that, different from the classical cosmology, the evolution of the large-scales non-adiabatic entropy perturbation can be driven by an adiabatic curvature perturbation and this adiabatic source for the non-adiabatic perturbation is a quantum effect. As an application of the related formalism, we study a decay model and give out the numerical results.