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

Fifth forces and broken scale symmetries in the Jordan frame