  The Wheeler-DeWitt Equation represents a tool to study Quantum Gravity and
Quantum Cosmology. Its solution in a very general context is, of course,
impossible. To this purpose we consider some distortions of General Relativity
like Gravity's Rainbow, Varying Speed of Light Cosmology, Generalized
Uncertainty Principle deformations and Ho\v{r}ava-Lifshitz gravity which could
allow the calculation of some observables like the cosmological constant. For
simplicity we consider only the Mini-Superspace approach related to a
Friedmann-Lema\^itre-Robertson-Walker space-time.
