Numerical Analysis of the Wave Function of the Multidimensional Universe
  In the framework of the Hartle-Hawking no-boundary proposal, we investigate quantum creation of the multidimensional universe with the cosmological constant $\Lambda$ but without matter fields. In this paper we solved the Wheeler-de Witt equation numerically. We find that the universe in which both of the spaces expand exponentially is the most probable in this model. 
Hirotaka Ochiai and Katsuhiko Sato