Axion monodromy inflation with multi-natural modulations

We study parameter space in the axion monodromy inflation corrected by nautically generated terms involving with the axion. The potential has the linear term with multiple sinusoidal functions, which play a role in generating modulations. We show that this potential leads both to a large tensor-to-scalar ratio r(T) similar to 0.16 and to a large negative running of spectral index alpha(s) similar to -(0.02 - 0.03), ameliorating the tension between the result of the PLANCK and that of the BICEP2. To realize these results, a small hierarchy among dynamical scales is required whereas the decay constants in sinusoidal functions remain sub-Planckian in this model. We discuss also reheating process after the inflation in a bottom-up approach.