Constraints on the generalized natural inflation after Planck 2018 *

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Abstract
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 ns and the tensor-to scalar ratio r for the CDM 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 at 68% confidence level (CL), and at 95% CL. We find that the GNI model is favored by P18 and BK15 in the ranges and 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.

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