  Forthcoming projects such as the DES, a JDEM, and LSST, aim to measure weak
lensing shear correlations with unprecedented accuracy. Weak lensing
observables are sensitive to both the distance-redshift relation and the growth
of structure in the Universe. If the cause of accelerated cosmic expansion is
dark energy within general relativity (GR), both cosmic distances and structure
growth are governed by the properties of dark energy. Consequently, one may use
lensing to check for this consistency and test GR. After reviewing the
phenomenology of such tests, we address one major challenge to such a program.
The evolution of the baryonic component of the Universe is highly uncertain and
can influence lensing observables, manifesting as modified structure growth for
a fixed cosmic distance scale. Using two proposed methods, we show that one
could be led to reject the null hypothesis of GR when it is the true theory if
this uncertainty in baryonic processes is neglected. Recent simulations suggest
that we can correct for baryonic effects using a parametrized model in which
the halo mass-concentration relation is modified. The correction renders biases
small compared to statistical uncertainties. We study the ability of future
weak lensing surveys to constrain the internal structures of halos and test the
null hypothesis of GR simultaneously. Compared to nulling information from
small-scales to mitigate sensitivity to baryonic physics, this internal
calibration program should provide limits on deviations from GR that are
several times more constraining. Specifically, we find that limits on general
relativity in the case of internal calibration are degraded by only ~30% or
less compared to the case of perfect knowledge of nonlinear structure.
