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

TL;DR

This paper demonstrates that generalized Proca vector fields cannot be consistently coupled to degenerate scalar-tensor gravitational theories without losing essential constraints, highlighting fundamental limitations in such interactions.

Contribution

It provides a proof that generalized Proca fields cannot be coupled to degenerate scalar-tensor theories without violating their degeneracy constraints.

Findings

Coupling to Christoffel connection causes loss of degeneracy constraints

Proca fields cannot be consistently integrated into degenerate scalar-tensor frameworks

Fundamental limitations on vector-scalar-tensor theory interactions

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.