  Future weak lensing surveys will map the evolution of matter perturbations
and gravitational potentials, yielding a new test of general relativity on
cosmic scales. They will probe the relations between matter overdensities,
local curvature, and the Newtonian potential. These relations can be modified
in alternative gravity theories or by the effects of massive neutrinos or
exotic dark energy fluids. We introduce two functions of time and scale which
account for any such modifications in the linear regime. We use a principal
component analysis to find the eigenmodes of these functions that cosmological
data will constrain. The number of constrained modes gives a model-independent
forecast of how many parameters describing deviations from general relativity
could be constrained, along with $w(z)$. The modes' scale and time dependence
tell us which theoretical models will be better tested.
