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Loop quantum cosmology with a scalar field is known to be closely linked withan inflationary phase. In this article, we study probabilistic predictions forthe duration of slow-roll inflation, by assuming a minimalist massive scalarfield 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 findthat the probability for a given number of inflationary e-folds is quitesharply peaked around 145, which is consistent with the most favored minimumvalues. In this precise sense, a satisfactory inflation is therefore a clearprediction of loop gravity. In addition, we derive an original and stringentupper limit on the Barbero-Immirzi parameter. The general picture of inflation,superinflation, deflation, and superdeflation is also much clarified in theframework of bouncing cosmologies.

Duration of inflation and conditions at the bounce as a prediction of effective isotropic loop quantum cosmolog