  The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is
applied to cosmological models in the minisuperspace. The quantization
procedure is performed explicitly for quantum cosmology in a flat
minisuperspace. The de Sitter cosmological model is worked out in detail and
the computation of the Wigner functions for the Hartle-Hawking, Vilenkin and
Linde wave functions are done numerically. The Wigner function is analytically
calculated for the Kantowski-Sachs model in (non)commutative quantum cosmology
and for string cosmology with dilaton exponential potential. Finally, baby
universes solutions are described in this context and the Wigner function is
obtained.
