Quantum cosmology with a nonlinear Born-Infeld type scalar field

A quantum model of gravitation interacting with a Born-Infeld type nonlinear scalar field phi is considered. The corresponding Wheeler-DeWitt equation can be solved analytically for both large and small phi-over-dot. In the extreme limits 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 largest possible vacuum energy and the largest interaction between the particles of the nonlinear scalar field.