Covariant Effective Action for Generalized Proca Theories

We investigate quantum stability of the generalised Proca theories in curved spacetime treating gravity as a dynamical field. To compute the quantum gravitational corrections we evaluate divergent part of the effective action at one loop level. We employ Vilkovisky-DeWitt formalism for this task which gives us a gauge invariant and gauge condition independent effective action. It is shown that the quantum corrections are suppressed by a UV cutoff parametrically higher than the Proca mass if the coupling constants are restricted to lie in a certain range. Furthermore it is shown that the quantum corrections remain suppressed even at scales where classical non-linearities dominate over kinetic terms allowing Vainshtein mechanism to work.