  Motivated by the recent CMB $B$-mode observation announced by the BICEP2
collaboration, we study simple inflationary models in the Randall-Sundrum
brane-world cosmology. Brane-world cosmological effects alter the inflationary
predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$)
from those obtained in the standard cosmology. In particular, the
tensor-to-scalar ratio is enhanced in the presence of the 5th dimension, and
simple inflationary models which predict small $r$ values in the standard
cosmology can yield $r$ values being compatible with the BICEP2 result,
$r=0.2^{+0.07}_{-0.05}$. Confirmation of the BICEP2 result and more precise
measurements of $n_s$ and $r$ in the near future allow us to constrain the
5-dimensional Planck mass ($M_5$) of the brane-world scenario. We also discuss
the post inflationary scenario, namely, reheating of the universe through
inflaton decay to the Standard Model particles. When we require the
renormalizability of the inflationary models, the inflaton only couples with
the Higgs doublet among the Standard Model fields, through which reheating
process occurs. If $M_5$ is as low as $10^6$ GeV, the mass of inflaton becomes
of ${\cal O}$(100 GeV), providing the inflationary predictions being consistent
with the BICEP2 and Planck results. Such a light inflaton has some impacts on
phenomenology at the electroweak scale through the coupling with the Higgs
doublet.
