On the stability and causality of scalar-vector theories
  Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations, such models require to introduce non-standard couplings between vector fields on the one hand, and either gravity or scalar fields on the other hand. In this article, we study models involving a vector field coupled to a scalar field. We derive restrictive necessary conditions for these models to be both stable (Hamiltonian bounded by below) and causal (hyperbolic equations of motion). 
Pierre Fleury, Juan P. Beltran Almeida, Cyril Pitrou, Jean-Philippe   Uzan
hep-th astro-ph.CO gr-qc