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We study and estimate probabilistic predictions for the duration of thepreinflationary and slow-roll phases after the bounce in loop quantumcosmology, determining how the presence of radiation in the prebounce phaseaffects these results. We present our analysis for different classes ofinflationary potentials that include the monomial power-law chaotic type ofpotentials, namely, for the quadratic, quartic and sextic potentials and alsofor a Higgs-like symmetry breaking potential, considering different values forthe vacuum expectation value in the latter case. We obtain the probabilitydensity function for the number of inflationary e-folds and for other relevantquantities for each model and produce probabilistic results drawn from thesedistributions. This study allows us to discuss under which conditions eachmodel could eventually lead to observable signatures on the spectrum of thecosmic microwave background, or, else, be also excluded for not predicting asuffcient amount of accelerated expansion. The effect of radiation on thepredictions for each model is explicitly quantified. The obtained resultsindicate that the number of inflationary e-folds in loop quantum cosmology isnot a priori an arbitrary number, but can in principle be a predictablequantity, even though the results are dependent on the model and on the amountof radiation in the Universe prior to the start of the inflationary regime.

Warm bounce in loop quantum cosmology and the prediction for the duration of inflation