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.
