Analysis of the Wheeler-DeWitt equation beyond planck scale and dimensional reduction

We solve the Wheeler-DeWitt equation for four-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or with a very large curvature beyond a Planck scale expectation values of operators are reduced to calculations in a path integral representation of three-dimensional Einstein gravity.