Constraining non-minimally coupled $\beta$-exponential inflation with CMB data

The $\beta$-exponential inflation is driven by a class of primordial potentials, derived in the framework of braneworld scenarios, that generalizes the well-known power law inflation. In this paper we update previous constraints on the minimal coupled $\beta$-exponential model [1] and extend the results also deriving the equations for the non-minimal coupled scenario. The predictions of both models are tested in light of the latest temperature and polarization maps of the Cosmic Microwave Background and clustering data. We also compare the predictions of these models with the standard $\Lambda$CDM model using the deviance information criterion (DIC), and find that the observational data show a moderate preference for the non-minimally coupled $\beta$-exponential inflationary model.