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We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bang and Big Crunch singularities are not traversable.
Using the ADM formalism in the minisuperspace, we obtain the commutative and noncommutative exact classical solutions and exact wave function to the Wheeler-DeWitt equation with an arbitrary factor ordering, for the anisotropic Bianchi type I cosmolo
The important role of scalar field in cosmology was noticed by a number of authors. Due to the fact that the scalar field possesses zero spin, it was basically considered in isotropic cosmological models. If considered in an anisotropic model, the li
We exactly solve the Wheeler-DeWitt equation for the closed homogeneous and isotropic quantum cosmology in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle. This form of generalized uncert
Aspects of non-linear Schr{o}dinger-type (NLS) formulation of scalar (phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big Rip singularity are presented. Slow-roll parameters for the curvature and barotropic density terms ar
We study relations between hydrodynamical (H) and scalar field (SF) models of the dark energy in the early Universe. Main attention is paid to SF described by the canonical Lagrangian within the homogeneous isotropic spatially flat cosmology. We anal