Observational Status of Tachyon Natural Inflation and Reheating

We study observational viability of Natural Inflation with a tachyon field as inflaton. By obtaining the main perturbation parameters in this model, we perform a numerical analysis on the parameter space of the model and in confrontation with $68\%$ and $95\%$ CL regions of Planck2015 data. By adopting a warped background geometry, we find some new constraints on the width of the potential in terms of its height and the warp factor. We show that the Tachyon Natural Inflation in the large width limit recovers the tachyon model with a $\phi^{2}$ potential which is consistent with Planck2015 observational data. Then we focus on the reheating era after inflation by treating the number of e-folds, temperature and the effective equation of state parameter in this era. Since it is likely that the value of the effective equation of state parameter during the reheating era to be in the range $0\leq \omega_{eff}\leq \frac{1}{3}$, we obtain some new constraints on the tensor to scalar ratio as well as the e-folds number and reheating temperature in this Tachyon Natural Inflation model.