  In loop quantum cosmology (LQC) the big bang is replaced by a quantum bounce
which is followed by a robust phase of super-inflation. Rather than growing
unboundedly in the past, the Hubble parameter \emph{vanishes} at the bounce and
attains a \emph{finite universal maximum} at the end of super-inflation. These
novel features lead to an unforeseen implication: in presence of suitable
potentials all LQC dynamical trajectories are funneled to conditions which
virtually guarantee slow roll inflation with more than 68 e-foldings, {without
any input from the pre-big bang regime}. This is in striking contrast to
certain results in general relativity, where it is argued that the a priori
probability of obtaining a slow roll with 68 or more e-foldings is suppressed
by a factor $e^{-204}$.
