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 pre-bounce 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 either eventually lead to observable signatures in the spectrum of the cosmic microwave background, or be excluded for not predicting a sufficient 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 the amount of radiation in the Universe prior to the start of the inflationary regime.