# Inflation with Derivative Self-interaction and Coupling to Gravity

## TL;DR

This paper explores a subclass of Horndeski theories with derivative self-interactions and non-minimal derivative couplings to gravity, analyzing their effects on inflationary observables and compatibility with current data.

## Contribution

It introduces a specific relation between derivative self-interaction and gravitational coupling, deriving observable predictions and constraining inflation models with data.

## Key findings

- Tensor-to-scalar ratio is suppressed by a factor of (1+1/γ).
- Models remain consistent with observational data due to this suppression.
- Derived constraints on chaotic and natural inflation models.

## Abstract

We consider a subclass of Horndeski theories for studying cosmic inflation. In particular, we investigate models of inflation in which the derivative self-interaction of the scalar field and the non-minimal derivative coupling to gravity are present in the action and equally important during inflation. In order to control contributions of each term as well as to approach the single-term limit, we introduce a special relation between the derivative interaction and the coupling to gravity. By calculating observable quantities including the power spectra and spectral tilts of scalar and tensor perturbation modes, and the tensor-to-scalar ratio, we found that the tensor-to-scalar ratio is suppressed by a factor of $(1+1/\gamma)$, where $\gamma$ reflects the strength of the derivative self-interaction of the inflaton field with respect to the derivative coupling gravity. We placed observational constraints on the chaotic and natural inflation models and showed that the models are consistent with the current observational data mainly due to the suppressed tensor-to-scalar ratio.