Testing general relativity at cosmological scales: Implementation and parameter correlations

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 the parametrized modified growth equations and their evolution. We implement known functional and binning approaches, and propose a new hybrid approach to evolve the 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 Hubble Space Telescope Cosmic Evolution Survey weak gravitational 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.