Cosmic Microwave Background constraints on non-minimal couplings in inflationary models with power law potentials

Inflationary models with power-law potentials are starting to be severely constrained by the recent measurements of Cosmic Microwave Background anisotropies provided by the Planck Satellite and by the BICEP2 telescope. In particular, models with power-law potentials $V(arphi)propto arphi^n$ with $n ge 2$ are strongly disfavored by present data since they predict a sizable contribution of gravitational waves with a tensor/scalar ratio of $rsim0.15$ that is at odds with current limits. A non-minimal coupling to gravity has been proposed as a physical mechanism to lower the predictions for $r$. In this paper we further investigate the issue, presenting constraints on non-minimal couplings from current CMB data under the assumption of power-law potentials. We found that models with $n>2$ show a statistically significant indication (above $95 %$ C.L.) for a non minimal coupling. Non minimal coupling is also preferred by models with $n<2$ albeit just at about $68 %$ C.L.. Interestingly, all the models considered show a non-zero running of the spectral index, $ n_ m run$, consistent with the 2018 Planck release value of $-0.007 pm 0.0068$. We point out how future accurate measurement of $ n_ m run$ would be necessary to significantly constraint these models and eventually rule out some or all of them. The combination of Planck data with the Bicep/Keck dataset strengthen these considerations.