Time emergency by self-measurement in a quantum anisotropic universe

The authors calculate Halliwell's propagator in the case of Mixmaster universe with small anisotropy and introduce terms that comprise the self-measurement of the universe of this model by higher multipoles of matter. Analyzing self-measurement with restricted path integral formalism Halliwell's modified propagator is obtained and a gauge-invariant physical time emerges as a consequence of this process. The conditions leading to Wheeler-DeWitt dynamics are also obtained. The comparison of these results with those of the isotropic case will enable to conclude that the number of conditions to be satisfied in order to have Halliwell's regime in the anisotropic situation bigger than in an isotropic universe. The terms of the parameters of the measurement process an expression for the threshold in time beyond which the scale factors of this model are meaningless