Future surveys, combining galaxy number counts and weak lensing measurements, will map the evolution of matter perturbations and gravitational potentials from the matter dominated epoch until today. This will tighten the constraints on allowed expansion histories, and test the relationships between matter overdensities, local curvature, and the Newtonian potential. These relationships, given by Einstein's equations of General Relativity, can be modified in alternative gravity theories, or by the effects of massive neutrinos or exotic forms of Dark Energy. We introduce two arbitrary functions of time and scale which can account for any such modifications in the linear regime. We use a principal component analysis to find the eigenmodes of these functions that surveys like DES and LSST, along with CMB and SN data, will constrain. The scale and time dependence of the well-constrained modes tell us which theoretical models will be better tested.