Fractional chaotic inflation in the lights of PLANCK and BICEP2
  In the lights of current BICEP2 observations accompanied with the PLANCK
satellite results, it has been observed that the simple single field chaotic
inflationary models provide a good agreement with their spectral index n_s and
large tensor-to-scalar ratio r (0.15 <r <0.26). To explore the other simple
models, we consider the fractional-chaotic inflationary potentials of the form
V_0 phi^(a/b) where a and b are relatively prime. We show that such kind of
inflaton potentials can be realized elegantly in the supergravity framework
with generalized shift symmetry and a nature bound a/b < 4 for consistency.
Especially, for the number of e-folding from 50 to 60 and some a/b from 2 to 3,
our predictions are nicely within at least 1 $\sigma$ region in the r-n_s
plane. We also present a systematic investigation of such chaotic inflationary
models with fractional exponents to explore the possibilities for the
enhancement in the magnitude of running of spectral index (\alpha_{n_s}) beyond
the simplistic models.
