Khalatnikov, I. M. Complex scalar field in quantum cosmology: from instanton to inflation. (English) Zbl 0988.83028 Acta Phys. Pol. B 30, No. 10, 3009-3027 (1999). Summary: We investigate the cosmological model with the complex scalar self-interacting inflaton field non-minimally coupled to gravity. The different geometries of the Euclidean classically forbidden regions are represented. The instanton solutions of the corresponding Euclidean equations of motion are found by numerical calculations supplemented by the qualitative analysis of Lorentzian and Euclidean trajectories. The applications of these solutions to the no-boundary and tunneling proposals for the wave function of the universe are studied. Possible interpretation of obtained results and their connection with inflationary cosmology is discussed. MSC: 83C45 Quantization of the gravitational field 81V17 Gravitational interaction in quantum theory PDFBibTeX XMLCite \textit{I. M. Khalatnikov}, Acta Phys. Pol. B 30, No. 10, 3009--3027 (1999; Zbl 0988.83028)