Since the dark energy problem has so far defied all attempts to find a simple and convincing solution, scientists have started to wonder whether the observed accelerated expansion of the universe is really due to some kind of extra fluid-like contribution, or rather a sign that General Relativity (GR) itself breaks down on large scales. This could happen in a variety of ways. For example, the universe itself could be higher-dimensional, all matter only existing on a three-dimensional hypersurface or brane, a scenario that is connect to String Theory. Alternatively, gravitons (the particles associated to the gravitational force) could be massive which might lead to a weakening of gravity over large distances -- such a scenario may be possible with the help of Galileons. Another possibility is that the Einstein-Hilbert action that describes GR is incomplete and needs to be modified in some way, leading to so-called f(R) and similar approaches, which in turn are linked to scalar-tensor theories. Unfortunately modifications of gravity suffer from problems similar to the ones affecting dark energy models: within an overabundance of ideas and possibilities, there is yet a lack of a really compelling scenario.
For this reason many cosmologists focus on experimental tests and characterizations of the dark sector: we can always cast the effective 3+1 dimensional equations that link the geometry of space-time to the matter content of the universe into the form of the usual Einstein equation of GR, but with an extra energy-momentum tensor (EMT) on the right hand side, into which we put all the extra contributions that might be due to a modification of GR. The goal then becomes on the one hand to predict how this extra EMT looks like (for example, modified gravity scenarios appear to generically create extra anisotropic stresses) and on the other hand to measure it with the help of observations. Two missions that our group are actively involved in are the Planck satellite to measure the CMB and the Euclid satellite to observe the large-scale structure with the help of a galaxy survey and weak lensing measurements.
Finally it should be mentioned that modifications of gravity have also been used to replace dark matter and to explain the flatness of the rotation curves of gravity, most notably with the help of MOND (modified Newtonian dynamics) and its relativistic extension TeVeS. This is not really an active research topic of our group at this time, and so we restrict the meaning of Modified Gravity scenarios to the above definition, i.e. as a way to explain the dark energy.