Conformally Invariant Cosmology Based on Riemann-Cartan Spacetime
  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. 
Yuri V. Shtanov (Brown University) and Sergei A. Yushchenko   (Bogolyubov Institute, Kiev)