Dark energy and normalization of cosmological wave function in modified gravitations

Based on Wheeler-DeWitt equation derived from general relativity, it had been found that only dark energy can lead to a normalizable cosmological wave function. It is shown in the present work that, for dRGT gravity, Eddington-inspired-Born-Infeld gravity and Ho$\check{\text{r}}$ava-Lifshitz gravity, the previous conclusion can also stand well in quantum cosmology induced from these modified gravities. This observation implies that there might be a universal relation between dark energy and normalizability of the cosmological wave function.