Quantum torsion with non-zero standard deviation: non-perturbative   approach for cosmology
  Cosmology with non-perturbative quantum corrections resulting from torsion is considered. It is shown that the evolution of closed, open and flat Universes is changed because of the presence of a non-zero dispersion of quantum torsion. The evolution of a Universe with quantum torsion and with one type of average curvature can be similar to the evolution of a Universe without quantum torsion and with another type of average curvature. For the description of the non-perturbative quantum torsion, a vector field approximation is applied. 
V. Dzhunushaliev, V. Folomeev, B. Kleihaus and J. Kunz
gr-qc hep-th