Constraints on the generalized natural inflation after Planck 2018

Based on the dynamics of single scalar field slow-roll inflation and the theory of reheating, we investigate the generalized natural inflationary (GNI) model. We introduce constraints on the scalar spectral index \begin{document}$n_{s}$\end{document} and the tensor-to scalar ratio r for the \begin{document}$\Lambda$\end{document}CDM \begin{document}$+r$\end{document} model, according to the latest data from Planck 2018 TT, TE, EE+low E+lensing (P18) and BICEP2/Keck 2015 season (BK15), i.e., with \begin{document}$n_{s}=0.9659\pm0.0044$\end{document} at 68% confidence level (CL), and \begin{document}$r<0.0623$\end{document} at 95% CL. We find that the GNI model is favored by P18 and BK15 in the ranges \begin{document}$\log_{10}(f/M_{p})= 0.62^{+0.17}_{-0.18}$\end{document} and \begin{document}$m=0.35^{+0.13}_{-0.23}$\end{document} at 68% CL. In addition, the corresponding predictions of generalized and two-phase reheating are discussed. It follows that the parameter m has significant effect on the model behavior.