Instabilities in Horndeski Yang-Mills inflation

Understand

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.