  We study the origin of fifth forces in scalar-tensor theories of gravity in
the so-called Jordan frame, where the modifications to the gravitational sector
are manifest. We focus on theories of Brans-Dicke type in which an additional
scalar field is coupled directly to the Ricci scalar of General Relativity. We
describe how the necessary diffeomorphism invariance of the modified
gravitational sector leads to a modification of the usual gauge fixing term
(for the harmonic gauge), as compared to Einstein gravity. This allows us to
perform a consistent linearization of the gravitational sector in the
weak-field limit, which gives rise to a kinetic mixing between the
non-minimally coupled scalar field and the graviton. It is through this mixing
that a fifth force can arise between matter fields. We are then able to compute
the matrix elements for fifth-force exchanges directly in the Jordan frame,
without the need to perform a conformal transformation to the so-called
Einstein frame, where the gravitational sector is of Einstein-Hilbert form. We
obtain results that are in agreement with the equivalent Einstein-frame
calculations and illustrate, still in the Jordan frame, the pivotal role that
sources of explicit scale symmetry breaking in the matter sector play in
admitting fifth-force couplings.
