Abstract
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.
Highlights
The extension of general relativity (GR) by additional light degrees of freedom is arguably the most natural way to provide a dynamical explanation of dark energy, thereby dispensing with the cosmological constant as the source of the observed late-time cosmic acceleration
The main assumptions are the following: (i) We focus exclusively on the so-called quadratic DHOST class, i.e., scalar–tensor theories whose Lagrangians involve operators that are at most quadratic in ∇2 φ. (ii) We consider a truncated version of Generalized Proca (GP) theory with at most cubic derivative self-interactions; (iii) the GP vector field couples with the DHOST sector only through the metric tensor
We have demonstrated that generalized Proca fields described by GP theory do not allow for a consistent coupling with a gravitational sector given by the DHOST class of models
Summary
The extension of general relativity (GR) by additional light degrees of freedom is arguably the most natural way to provide a dynamical explanation of dark energy, thereby dispensing with the cosmological constant as the source of the observed late-time cosmic acceleration. The complete classification of scalar–tensor theories seems to be an interesting and timely theoretical problem In this effort, the assumption of having precisely three local degrees of freedom—two propagated by the metric and one by the scalar field—severely restricts the space for possible models. DHOST theories provide, a very interesting solution to the classification problem of scalar–tensor gravity They are consistent theories within the scope of that problem, at least according to the way we have formulated it, it is clear that physical consistency will reduce the space of allowed models by the imposition of further constraints. The mixing with matter fields can obstruct this constraint, leading to the reappearance of the ghost degree of freedom and an inconsistent theory [34] This may occur even if matter is minimally coupled with the metric tensor, for an indirect coupling with the DHOST scalar is still present. We will come back to this point in the final discussion
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