On the Coupling of Generalized Proca Fields to Degenerate Scalar-Tensor Theories

We prove that vector fields described by the generalized Proca class of theories do not admit consistent coupling with a gravitational sector defined by a scalar-tensor theory of the degenerate type. Under the assumption that there exists a frame in which the Proca field interacts with gravity only through the metric tensor, our analysis shows that at least one of the constraints associated with the degeneracy of the scalar-tensor sector is inevitably lost whenever the vector theory includes coupling with the Christoffel connection.

Automated summary

Our analysis shows that coupling between vector fields described by the generalized Proca class of theories and a gravitational sector defined by a scalar-tensor theory of the degenerate type leads to the loss of at least one constraint associated with the scalar-tensor sector.