Conformal Anisotropic Quantum Cosmology

Abstract

In this paper we apply the ideas put forward by Ho\v{r}ava, and introduce anisotropic transformations to cosmology. We start with the Kantowski-Sachs cosmological model and impose anisotropic transformation invariance on the minisuperspace variables. We study the symmetries of the anisotropic model and by canonical quantization find a Schr\"odinger type equation for $z\ne 1$. Finally, we conclude that introducing anistropic invariance can be considered a solution to the problem of time in quantum cosmology and gives some insight on the structure of a well behaved quantum theory of gravity.