  Conformally invariant GUT-like model including gravity based on Riemann -
Cartan space-time $U_4$ is considered. Cosmological scenario that follows from
the model is discussed and standard quantum gravitational formalism in the
Arnowitt-Deser-Misner form is developed. General formalism is then illustrated
on Bianchi-IX minisuperspace cosmological model. Wave functions of the universe
in the de Sitter minisuperspace model with Vilenkin and Hartle-Hawking boundary
conditions are considered and corresponding probability distributions for the
scalar field values are calculated.
