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

We study and estimate probabilistic predictions for the duration of the preinflationary and slow-roll phases after the bounce in loop quantum cosmology, determining how the presence of radiation in the prebounce phase affects these results. We present our analysis for different classes of inflationary potentials that include the monomial power-law chaotic type of potentials, namely, for the quadratic, quartic and sextic potentials and also for a Higgs-like symmetry breaking potential, considering different values for the vacuum expectation value in the latter case. We obtain the probability density function for the number of inflationary e-folds and for other relevant quantities for each model and produce probabilistic results drawn from these distributions. This study allows us to discuss under which conditions each model could eventually lead to observable signatures on the spectrum of the cosmic microwave background, or, else, be also excluded for not predicting a suffcient amount of accelerated expansion. The effect of radiation on the predictions for each model is explicitly quantified. The obtained results indicate that the number of inflationary e-folds in loop quantum cosmology is not a priori an arbitrary number, but can in principle be a predictable quantity, even though the results are dependent on the model and on the amount of radiation in the Universe prior to the start of the inflationary regime.