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

## TL;DR

This study investigates how non-minimal couplings in power-law inflationary models can reconcile predictions with recent CMB observations, highlighting the significance of non-minimal couplings especially for models with n>2.

## Contribution

The paper provides new constraints on non-minimal couplings in power-law inflation models using current CMB data, emphasizing their role in models with n≠2.

## Key findings

- Models with n>2 show significant non-minimal coupling indications.
- Models with n<2 also favor non-minimal coupling but less strongly.
- All models exhibit a non-zero spectral index running consistent with Planck data.

## Abstract

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.