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.