Vector theories in cosmology

This article provides a general study of the Hamiltonian stability and the hyperbolicity of vector field models involving both a general function of the Faraday tensor and its dual, f(F²,FF), as well as a Proca potential for the vector field, V(A²). In particular it is demonstrated that theories involving only f(F²) do not satisfy the hyperbolicity conditions. It is then shown that in this class of models, the cosmological dynamics always dilutes the vector field. In the case of a nonminimal coupling to gravity, it is established that theories involving Rf(A²) or Rf(F²) are generically pathologic. To finish, we exhibit a model where the vector field is not diluted during the cosmological evolution, because of a nonminimal vector field-curvature coupling which maintains second-order field equations. The relevance of such models for cosmology is discussed.