General Relativity (GR) is a dynamical theory of spacetime, matter (in the largest meaning, ie including electromagnetic fields, scalar fields, ...) acting as the spacetime curvature source. Through the Einstein's equation, matter is coupled to the metric tensor, that encodes all the spacetime geometric properties (ie both metric and local parallelism properties). In the framework of this theory, motions under gravity are nothing but inertial motions in the resulting curved spacetime.
The theory has proved to give a very accurate description of both the motion of massive and non massive (like photon's in the usual electromagnetic theory) bodies. Nowadays, GR is then the natural framework for both celestial mechanics and astrometry problems. The theory is also very succesful in describing compact astrophysical bodies (condensed stars, ultimately black holes), the dynamics of our Universe (both as a whole and in the dynamics of its substructures) and in the gravitational lensing. Another striking success was the interpretation of the recently detected gravitational waves: the different phases of the observed signals fit remarkably well with the final stages expected from binary black holes dynamics and merging.
Nevertheless, some questions remain, questionning on the GR's validity domain. From the observational side, the accelerated expansion of the Universe strongly suggests that the GR theory should be modified, at least by adding a cosmological constant, but maybe in a more radical way. From the theoretical side, the main trouble comes from the conceptual framework of GR: as the source of gravity, matter is described just ignoring its quantum nature. Considering, along the lines of GR, matter as source of gravity, but taking in the same time its quantum behaviour into account, requires describing the spacetime properties in a quantum framework in some way. Formulating such a theory remains one of the most challenging issue in theoretical physics.
Thence, paying attention to alternatives to GR makes sense. In this context, the so called scalar-tensor (ST) theories, in which the Newton's constant is replaced by a scalar field, deserve a special attention, for at least two reasons. First, several attempts to quantize gravity, in a unified (with the other interactions of nature) scheme or not, returns an ST like (rather than GR) classical gravity sector. Second, ST theories are, to some extent, able to encompass the GR observational successes, since their solutions behave like GR ones in well suited conditions. From the phenomenological point of view, the scalar entering ST theories determines the local value of the Newton's "constant", that is then dependent on the place and the date where and at which it is measured. The links between ST and GR theories is not an obvious task, and is one of the research fields in our team.