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Complex inflation field in quantum cosmology. (English) Zbl 0936.83053

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 interpretations of the results obtained and their connection with inflationary cosmology are discussed. The restrictions on the possible values of the new quasifundamental constant of the theory – non-zero classical charge – are obtained. The equations of motion for the generalized cosmological model with complex scalar field are written down and investigated. The conditions of the existence of instanton solutions corresponding to permanent values of an absolute value of scalar field are obtained.

MSC:

83F05 Relativistic cosmology
81V17 Gravitational interaction in quantum theory
83C45 Quantization of the gravitational field
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