CMB constraints on $\beta$-exponential inflationary models

We analyze a class of generalized inflationary models proposed in Ref. [1], known as $\beta$-exponential inflation. We show that this kind of potential can arise in the context of brane cosmology, where the field describing the size of the extra-dimension is interpreted as the inflaton. We discuss the observational viability of this class of model in light of the latest Cosmic Microwave Background (CMB) data from the Planck Collaboration through a Bayesian analysis, and impose tight constraints on the model parameters. We find that the CMB data alone prefer \textit{weakly} the minimal standard model ($\Lambda$CDM) over the $\beta$-exponential inflation. However, when current local measurements of the Hubble parameter, $H_0$, are considered, the $\beta$-inflation model is {\it moderately} preferred over the $\Lambda$CDM cosmology, making the study of this class of inflationary models interesting in the context of the current $H_0$ tension.