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 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.

Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling

“…Finally, we have noted, as a side remark, that in the presence of a galileon field in the matter sector, the dynamical scalar degree of freedom eliminated from the gravitational sector could reappear in a similar way to the case analyzed in Ref. [66,67]. The result of our analysis implies that a galileon field must be coupled nonminimally to gravity in the frame where the action takes the form of Eq.…”

“…This result shows that there are two scalar DOFs in the system unless cβ 1 = 0; the scalar DOF reappears in the presence of a galileon field if it is minimally coupled to gravity in the frame where β 1 = 0. What we have seen here is analogous to the issue pointed out in the context of degenerate higher-order scalar-tensor theories [66,67]. In the case of the degenerate higher-order scalar-tensor theories, the constraint associated with the degeneracy is lost if a matter field is coupled to the Christoffel symbol.…”

To Half--Be or Not To Be?

“…This is an interesting novelty of (E)PN theory relative to GP: the primary constraint is non-linear in the momenta 9 . The resulting base and augmented Hamiltonians are therefore…”

“…While the equations of motion generically include higher derivatives away from that limit, the presence of a non-trivial constraint ensures that the theory propagates the correct D − 1 number of degrees of freedom in D dimensions. These derivative self-interactions were shown to be responsible for genuinely new properties in relation to the screening mechanisms and the coupling to alternative theories of gravity [7][8][9], although the main motivation for the development of the theory was aimed at applications to astrophysical systems [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and cosmology [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42].…”

Cosmology of Extended Proca-Nuevo

“…It is worth emphasizing that the interactions of GP theory are non-trivial in that they are not simply constructed out of the field strength and the undifferentiated field, but includes derivative interactions that give rise to some unique properties, e.g. in relation to the screening mechanisms and the coupling to alternative theories of gravity [26][27][28].…”