Inflationary Solutions in Quantum Cosmology

We prove that in the Hartle-Hawking approach to quantum cosmology the existence of an inflationary phase is a general property of minisuperspace models given by a closed Friedmann-Robertson-Walker universe containing a massless scalar field with a $\lambda {\varphi }^n$ self-interaction. The evolution in time of the cosmic scale factor and of the scalar field in the very early universe is derived, together with the conditions to be satisfied in order to solve the horizon and flatness problems.