We study a semi-classical model of the mixmaster universe. We first derive
the quantum model and then introduce its semi-classical approximation. We
employ a general integral quantization method that respects the symmetries of
the model given by the affine and the Weyl-Heisenberg groups, and can produce a
wide class of quantum models. The semi-classical approximation is based on the
coherent states. The semi-classical dynamics is complex and can not be solved
by analytical methods. We focus on a key qualitative feature of the dynamics,
namely, we investigate whether the primordial anisotropic universe can undergo
a spontaneous inflationary phase driven by the anisotropic energy combined with
semi-classical corrections. The answer to this question provides a useful
perspective on the inflationary paradigm as well as on alternative bouncing
models.Comment: 15 pages, 6 figure