Cosmologies in Horndeski's second-order vector-tensor theory
  Horndeski derived a most general vector-tensor theory in which the vector
field respects the gauge symmetry and the resulting dynamical equations are of
second order. The action contains only one free parameter, $\lambda$, that
determines the strength of the non-minimal coupling between the gauge field and
gravity. We investigate the cosmological consequences of this action and
discuss observational constraints. For $\lambda<0$ we identify singularities
where the deceleration parameter diverges within a finite proper time. This
effectively rules out any sensible cosmological application of the theory for a
negative non-minimal coupling. We also find a range of parameter that gives a
viable cosmology and study the phenomenology for this case. Observational
constraints on the value of the coupling are rather weak since the interaction
is higher-order in space-time curvature.
