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.
