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 $V(\varphi)\propto \varphi^n$ 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 $r\sim0.15$
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_{\rm run}$, consistent with the 2018 Planck release value
of $-0.007 \pm 0.0068$. We point out how future accurate measurement of $
n_{\rm 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.
