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We prove that many cosmological models characterized by vectors nonminimallycoupled to the curvature (such as the Turner-Widrow mechanism for theproduction of magnetic fields during inflation, and models of vector inflationor vector curvaton) contain ghosts. The ghosts are associated with thelongitudinal vector polarization present in these models, and are found fromstudying the sign of the eigenvalues of the kinetic matrix for the physicalperturbations. Ghosts introduce two main problems: (1) they make the theoriesill-defined at the quantum level in the high energy/sub horizon regime (andcreate serious problems for finding a well behaved UV completion); (2) theycreate an instability already at the linearized level. This happens because theeigenvalue corresponding to the ghost crosses zero during the cosmologicalevolution. At this point the linearized equations for the perturbations becomesingular (we show that this happens for all the models mentioned above). Weexplicitly solve the equations in the simplest cases of a vector without vev ina FRW geometry, and of a vector with vev plus a cosmological constant, and weshow that indeed the solutions of the linearized equations diverge when theseequations become singular.

Ghost instabilities of cosmological models with vector fields nonminimally coupled to the curvature