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 L D Landau’s old ideas is analyzed. Particular attention is given to the oscillatory approach to singularity; quantum tunneling processes determining wave function of the Universe in the presence of a compex 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.

PACS: 98.80.Hw, 98.80.Bp, 04.60.Ds (all) DOI: 10.1070/PU1998v041n06ABEH000401 URL: https://ufn.ru/en/articles/1998/6/a/ 000075347000001 Citation: Khalatnikov I M, Kamenshchik A Yu "Singularity, initial conditions and quantum tunneling in modern cosmology" Phys. Usp. 41 525–542 (1998) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Халатников И М, Каменщик А Ю «Сингулярность, начальные условия и квантовое туннелирование в современной космологии» УФН 168 593–611 (1998); DOI: 10.3367/UFNr.0168.199806a.0593