  In this paper we investigate the cosmological dynamics of geometric inflation
by means of the tools of the dynamical systems theory. We focus in the study of
two explicit models where it is possible to sum the infinite series of higher
curvature corrections that arises in the formalism. These would be very
interesting possibilities since, if regard gravity as a quantum effective
theory, a key feature is that higher powers of the curvature invariants are
involved at higher loops. Hence, naively, consideration of the whole infinite
tower of curvature invariants amounts to consideration of all of the higher
order loops. The global dynamics of these toy models in the phase space is
discussed and the quantum origin of primordial inflation is exposed.
