Distinguishing between Extra Natural Inflation and Natural Inflation
  after BICEP2
  In this paper, we carefully calculated the tensor-to-scalar ratio, the
running spectral index, and the running of running spectrum for (extra) natural
inflation in order to compare with recent BICEP2 data, PLANCK satellite data
and future 21 cm data. We discovered that the prediction for running spectral
index and the running of running spectrum in natural inflation is different
from that in the case of extra natural inflation. Near future observation for
the running spectral index may achieve enough accuracy to allow us
distinguishing between extra natural inflation from natural inflation.
Distinguishing the models by using the running of running spectrum is not
impossible but would be more challenging for future experiments.
