In general relativity the gravitational field, i.e. the spacetime curvature, couples to all matter according to the principle of minimal coupling which states that the stress-energy tensors of all matter fields will act as sources for the gravitational field in the same way. For the formulation of the theory this means the matter fields intertwine with the gravitational field only in the simplest possible way and no type of matter is singled out by the form of its interaction with gravity.
Starting with the ideas of Nordström in 1914 physicists have been considering the possibility that the different interactions observed in nature can be unified in the sense that they can be derived from one fundamental underlying theory. Such a theory would naturally allow more complicated interactions between gravitation and matter. In unified theories one typically encounters scalar fields which couple non-minimally the gravitation. The effective low-energy theories arising in this context are denoted as scalar-tensor theories (tensor referring to the gravitational field). Scalar-tensor theories are fairly well constrained by the observation of binary pulsars and of the orbits of the solar-system planets. Hence one usually assumes that the putative scalar fields are kept at some fixed background value by a self-interaction which makes them effectively decouple from other matter fields.
There are however some tricks which might be realized by nature which would allow the scalar field to be dynamical under some circumstances (e.g. low gravitation, low temperatures). In this case the scalar could mediate an enhanced coupling between gravitation and some type of matter. A suggestion for a particular strong interaction has recently been put forward. It even postulates a measurable effect on gravity from the earth's magnetic field. Such a strong gravielectric coupling would however open dramatic technological possibilities including the possibility of electro-magnetic levitation.
These exiting possibilities in mind we have conducted a critical evaluation of such models. We derived constraints on such theories which do not rely on astronomical observations but on data from Eötvös experiments testing the universality of free fall. We found that these experiments give strong upper bounds on the strength of possible gravielectric couplings. These bounds result from the electric field that is present in every nucleus. If a gravielectric coupling were present the electric field of the nucleus would modify its effective gravitational mass. This modification would be of different strength for different elements and would thus show up as a different behaviour of test bodies of different materials but with the same inertial mass in Eötvös experiments. The constraints from experimental data demonstrate that a possible gravielectric coupling must be so weak that it is clearly not useful for technological applications. Although this result was derived for a gravielectric coupling mediated by a scalar field the arguments apply for gravielectric couplings in general.