On scalar and vector fields coupled to the energy-momentum tensor

We consider theories for scalar and vector _elds coupled to the energymomentum tensor. Since these _elds also carry a non-trivial energy-momentum tensor, the coupling prescription generates self-interactions. In analogy with gravity theories, we build the action by means of an iterative process that leads to an in_nite series, which can be resumed as the solution of a set of di_erential equations. We show that, in some particular cases, the equations become algebraic and that is also possible to _nd solutions in the form of polynomials. We briey review the case of the scalar _eld that has already been studied in the literature and extend the analysis to the case of derivative (disformal) couplings. We then explore theories with vector _elds, distinguishing between gaugeand non-gauge-invariant couplings. Interactions with matter are also considered, taking a scalar _eld as a proxy for the matter sector. We also discuss the ambiguity introduced by superpotential (boundary) terms in the de_nition of the energy-momentum tensor and use them to show that it is also possible to generate Galileon-like interactions with this procedure. We _nally use collider and astrophysical observations to set constraints on the dimensionful coupling which characterises the phenomenology of these models.