  In this paper the quantum cosmological consequences of introducing a term
cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are
investigated. It is argued that this term represents a more generic
perturbation to the action than the quadratic correction usually considered. A
qualitative argument suggests that there exists a region of parameter space in
which neither the tunneling nor the no-boundary boundary conditions predict an
epoch of inflation that can solve the horizon and flatness problems of the big
bang model. This is in contrast to the $R^2$--theory.
