  We study cosmological inflation and its dynamics in the framework of the
Randall-Sundrum II brane model. In particular, we analyze in detail four
representative small-field inflationary potentials, namely Natural inflation,
Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each
characterized by two mass scales. We constrain the parameters for which a
viable inflationary Universe emerges using the latest PLANCK results.
Furthermore, we investigate whether or not those models in brane cosmology are
consistent with the recently proposed Swampland Criteria, and give predictions
for the duration of reheating as well as for the reheating temperature after
inflation. Our results show that (i) the distance conjecture is satisfied, (ii)
the de Sitter conjecture and its refined version may be avoided, and (iii) the
allowed range for the five-dimensional Planck mass, $M_5$, is found to be
between $10^5~\textrm{TeV}$ and $10^{12}~\textrm{TeV}$. Our main findings
indicate that non-thermal leptogenesis cannot work within the framework of
RS-II brane cosmology, at least for the inflationary potentials considered
here.
