A Natural Inflation inspired model

We propose a modification of the Natural Inflation potential in such a way that the spontaneous symmetry breaking scale f can take values less than one (in Planck units). The proposed potential seems simple enough, however, its consequences are difficult to calculate analytically. Therefore, we illustrate the feasibility of the model by considering some numerical examples that easily satisfy the conditions imposed on the observables ns\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n_s$$\end{document} and r by the most recent observations, while at the same time maintaining the number of e-folds during the inflationary epoch within the expected range.