SINGULARITY, INITIAL CONDITIONS, QUANTUM TUNNELING AND SCALAR FIELD IN MODERN COSMOLOGY

We consider classical and quantum dynamics of cosmological models with complex and real scalar fields and compare ideas elaborated in the co urse of modem development of cosmology with those put forward 25 years ago in the cycle of papers devoted to oscillatory approach to singula rity. The peculiarities of the quantum tunneling processes determining the wave function of the Universe in the presence of complex scalar f ield is described in some detail. The classical dynamics of the simple cosmological model with real scalar field is investigated from the vi ewpoint of such properties as chaos, fractality and possibility of con struction of theory of perturbation around the kindred exactly solvabl e model.