2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35085Examples of nonsingular cosmological models are presented on the basis of exact solutions to multidimensional gravity equations. These examples involve pure imaginary scalar fields, or, in other terms, ``phantom'' fields with an unusual sign of the kinetic term in the Lagrangian. We show that, with such fields, hyperbolic nonsingular models with a cosmological bounce (unlike spherical and spatially flat models) emerge without special relations among the integration constants, i.e., without fine tuning. In such models, the extra-dimension scale factors as well as scalar fields evolve smoothly between different finite asymptotic values. Examples of theories which create phantom scalar fields are obtained from string-inspired multidimensional field models and from theories of gravity in integrable Weyl space-times.10 pages, submitted to Proc. Int. School GAS04, Kiten, Bulgaria, June 10-16, 2004General Relativity and Quantum Cosmologytext