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

Abstract

We prove that vector fields described by the generalized Proca class of theories do not admit a consistent coupling to 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 a coupling to the Christoffel connection.1 In the context of higher-derivative theories, it is worth remarking that the Starobinsky model of inflation provides a healthy and consistent example of this class [3]. See also [4][5][6] for related works on inflationary models based on generalized scalartensor theories.