# Instabilities in Horndeski Yang-Mills inflation

## TL;DR

This paper investigates a Horndeski Yang-Mills inflation model and finds that it suffers from ghost and Laplacian instabilities in tensor perturbations, making it an inconsistent inflationary scenario.

## Contribution

The study derives the second-order tensor perturbation action in HYM theory and demonstrates the unavoidable instabilities caused by the non-minimal coupling.

## Key findings

- Ghost instabilities in tensor sector during inflation
- Laplacian instabilities inside the Hubble radius
- HYM theory is not a viable inflationary model

## Abstract

A non-abelian $SU(2)$ gauge field with a non-minimal Horndeski coupling to gravity gives rise to a de Sitter solution followed by a graceful exit to a radiation-dominated epoch. In this Horndeski Yang-Mills (HYM) theory we derive the second-order action for tensor perturbations on the homogeneous and isotropic quasi de Sitter background. We find that the presence of the Horndeski non-minimal coupling to the gauge field inevitably introduces ghost instabilities in the tensor sector during inflation. Moreover, we also find Laplacian instabilities for the tensor perturbations deep inside the Hubble radius during inflation. Thus, we conclude that the HYM theory does not provide a consistent inflationary framework due to the presence of ghosts and Laplacian instabilities.