Axion-like particle inflation and dark matter

In this paper, we propose a generalized natural inflation (GNI) model to study axion-like particle (ALP) inflation and dark matter (DM). GNI contains two additional parameters $(n_1, n_2)$ in comparison with the natural inflation, that make GNI more general. The $n_1$ build the connection between GNI and other ALP inflation model, $n_2$ controls the inflaton mass. After considering the cosmic microwave background and other cosmological observation limits, the model can realize small-field inflation with a wide mass range, and the ALP inflaton considering here can serve as the DM candidate for certain parameter spaces.