Singularity, initial conditions and quantum tunneling in modern cosmology.

Mathematics – Logic

Scientific paper

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Cosmological Models

Scientific paper

The key problems of modern cosmology, such as the cosmological singularity, initial conditions, and the quantum tunneling hypothesis, are discussed. The relationship between the latest cosmological trends and Landau's old ideas is analyzed. Particular attention is given to the oscillatory approach to the singularity; quantum tunneling processes determining the wave function of the Universe in the presence of a complex scalar field; and the role of quantum corrections in these processes. The classical dynamics of closed models with a real scalar field is investigated from the standpoint of chaotic, fractal, and singularity-avoiding properties.

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