SINGULARITY, INITIAL CONDITIONS AND QUANTUM TUNNELING IN MODERN COSMOLOGY

Key problems of modern cosmology, such as the cosmological singularity , initial conditions, and the quantum tunneling hypothesis, are discus sed. The relationship between the latest cosmological trends and L D L andau's old ideas is analyzed. Particular attention is given to the os cillatory approach to singularity; quantum tunneling processes determi ning the Universe wave function in the presence of a complex scalar fi eld; and the role of quantum corrections in these processes. The class ical dynamics of closed models with a real scalar held is investigated from the standpoint of chaotic, fractal, and singularity-avoiding pro perties.