Conformal Anisotropic Quantum Cosmology

TL;DR

This paper explores anisotropic transformations in quantum cosmology, applying them to the Kantowski-Sachs model, and suggests they may address the problem of time in quantum gravity.

Contribution

It introduces anisotropic invariance into cosmological models and derives a Schrödinger-type equation, offering a new approach to quantum gravity.

Findings

Anisotropic invariance leads to a Schrödinger-type equation for the cosmological model.

The approach provides insights into the problem of time in quantum cosmology.

The model suggests a pathway for a well-behaved quantum theory of gravity.

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.