COMPLEX INFLATON FIELD IN QUANTUM COSMOLOGY

We investigate the cosmological model with the complex scalar self-int eracting inflaton field non-minimally coupled to gravity. The differen t geometries of the Euclidean classically forbidden regions are repres ented. The instanton solutions of the corresponding Euclidean equation s of motion are found by numerical calculations supplemented by the qu alitative analysis of Lorentzian and Euclidean trajectories. The appli cations of these solutions to the no-boundary and tunneling proposals for the wave function of the Universe are studied. Possible interpreta tion of obtained results and their connection with inflationary cosmol ogy is discussed. The restrictions on the possible values of the new q uasifundamental constant of the theory - non-zero classical charge - a re obtained. The equations of motion for the generalized cosmological model with complex scalar held are written down and investigated. The conditions of the existence of instanton solutions corresponding to pe rmanent values of an absolute value of scalar field are obtained.