  The testing of general relativity at cosmological scales has become a
possible and timely endeavor that is not only motivated by the pressing
question of cosmic acceleration but also by the proposals of some extensions to
general relativity that would manifest themselves at large scales of distance.
We analyze here correlations between modified gravity growth parameters and
some core cosmological parameters using the latest cosmological data sets
including the refined Cosmic Evolution Survey 3D weak lensing. We provide
parametrized modified growth equations and their evolution. We implement known
functional and binning approaches, and propose a new hybrid approach to evolve
modified gravity parameters in redshift (time) and scale. The hybrid
parametrization combines a binned redshift dependence and a smooth evolution in
scale avoiding a jump in the matter power spectrum. The formalism developed to
test the consistency of current and future data with general relativity is
implemented in a package that we make publicly available and call ISiTGR
(Integrated Software in Testing General Relativity), an integrated set of
modified modules for the publicly available packages CosmoMC and CAMB,
including a modified version of the integrated Sachs-Wolfe-galaxy cross
correlation module of Ho et al and a new weak-lensing likelihood module for the
refined HST-COSMOS weak lensing tomography data. We obtain parameter
constraints and correlation coefficients finding that modified gravity
parameters are significantly correlated with \sigma_8 and mildly correlated
with \Omega_m, for all evolution methods. The degeneracies between \sigma_8 and
modified gravity parameters are found to be substantial for the functional form
and also for some specific bins in the hybrid and binned methods indicating
that these degeneracies will need to be taken into consideration when using
future high precision data.
