Quantum cosmology with a nonlinear Born-Infeld type scalar field

A quantum model of gravitation interacting with a Born-Infeld type nonlinea r scalar field cp is considered. The corresponding Wheeler-DeWitt equation can be solved analytically for both large and small phi. In the extreme lim its of small and large cosmological scale factors the wave function of the Universe can also be obtained by applying the methods developed by Vilenkin and Hartle and Hawking. An inflationary Universe is predicted with the lar gest possible vacuum energy and the largest interaction between the particl es of the nonlinear scalar field.