  The next generation of weak lensing surveys will trace the evolution of
matter perturbations and gravitational potentials from the matter dominated
epoch until today. Along with constraining the dynamics of dark energy, they
will probe the relations between matter overdensities, local curvature, and the
Newtonian potential. We work with two functions of time and scale to account
for any modifications of these relations in the linear regime from those in the
LCDM model. We perform a Principal Component Analysis (PCA) to find the
eigenmodes and eigenvalues of these functions for surveys like DES and LSST.
This paper builds on and significantly extends the PCA analysis of Zhao et al.
(2009) in several ways. In particular, we consider the impact of some of the
systematic effects expected in weak lensing surveys. We also present the PCA in
terms of other choices of the two functions needed to parameterize modified
growth on linear scales, and discuss their merits. We analyze the degeneracy
between the modified growth functions and other cosmological parameters, paying
special attention to the effective equation of state w(z). Finally, we
demonstrate the utility of the PCA as an efficient data compression stage which
enables one to easily derive constraints on parameters of specific models
without recalculating Fisher matrices from scratch.
