  Loop quantum cosmology with a scalar field is known to be closely linked with
an inflationary phase. In this article, we study probabilistic predictions for
the duration of slow-roll inflation, by assuming a minimalist massive scalar
field as the main content of the universe. The phase of the field in its
"prebounce" oscillatory state is taken as a natural random parameter. We find
that the probability for a given number of inflationary e-folds is quite
sharply peaked around 145, which is consistent with the most favored minimum
values. In this precise sense, a satisfactory inflation is therefore a clear
prediction of loop gravity. In addition, we derive an original and stringent
upper limit on the Barbero-Immirzi parameter. The general picture of inflation,
superinflation, deflation, and superdeflation is also much clarified in the
framework of bouncing cosmologies.
