Inflationary models with non-minimally derivative coupling

TL;DR

This paper derives detailed spectral tilt formulas for inflationary models with non-minimal derivative coupling, showing how such models can achieve sub-Planckian field excursions and better fit observational data.

Contribution

It provides the second-order spectral tilt formulas without the high friction limit and demonstrates the observational viability of quartic potentials with non-minimal derivative coupling.

Findings

Energy scale is sub-Planckian due to non-minimal kinetic coupling.

Modified Lyth bound with an extra suppression factor.

Quartic potential models fit observations at 95% CL.

Abstract

We derive the general formulae for the the scalar and tensor spectral tilts to the second order for the inflationary models with non-minimally derivative coupling without taking the high friction limit. The non-minimally kinetic coupling to Einstein tensor brings the energy scale in the inflationary models down to be sub-Planckian. In the high friction limit, the Lyth bound is modified with an extra suppression factor, so that the field excursion of the inflaton is sub-Planckian. The inflationary models with non-minimally derivative coupling are more consistent with observations in the high friction limit. In particular, with the help of the non-minimally derivative coupling, the quartic power law potential is consistent with the observational constraint at 95\% CL.