  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 $\lambda\phi^{n}$ 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.
