A non-minimal coupling of a non-Abelian vector field to the gravitational sector may provide a novel framework to model inflation. However, on an isotropic quasi de Sitter solution, this Horndeski-Yang-Mills theory displays several inconsistencies in its tensor perturbations: including ghost and Laplacian instabilities which occur at unacceptable low scales (within one Hubble radius) during inflation.

Historically, inflation has been modeled with simple scalar fields. Higher spin fields are more complicated, but may also be present in the early Universe. Here we see that, with a single vector degree of freedom, one cannot support an inflationary period without exciting ghosts and gradient instabilities. This is then not a particularly favoured matter content for the early universe (which seems consistent with some period of inflation).