NONMINIMALLY COUPLED COMPLEX SCALAR FIELD IN CLASSICAL AND QUANTUM COSMOLOGY

We investigate a cosmological model with a complex scalar self-interac ting inflaton field non-minimally coupled to gravity. The different ge ometries of the Euclidean classically forbidden regions are represente d. The instanton solutions of the corresponding Euclidean equations of motion are found by numerical calculations. These solutions give rath er non-trivial examples of real tunnelling geometries. Possible interp retation of obtained results and their connection with inflationary co smology is discussed.