Figures of merit and constraints from testing general relativity using the latest cosmological data sets including refined COSMOS 3D weak lensing

We use cosmological constraints from current data sets and a figure of merit approach in order to probe any deviations from general relativity at cosmological scales. The figure of merit approach is used to study and compare the constraining power of various combinations of data sets on the modified gravity (MG) parameters. We use the recently refined HST-COSMOS weak-lensing tomography data, the ISW-galaxy cross correlations from 2MASS and SDSS luminous red galaxy surveys, the matter power spectrum from SDSS-DR7 (MPK), the WMAP7 temperature and polarization spectra, the baryon acoustic oscillations from Two-Degree Field and SDSS-DR7, and the Union2 compilation of type Ia supernovae, in addition to other bounds from Hubble parameter measurements and big bang nucleosynthesis. We use three parametrizations of MG parameters that enter the perturbed field equations. In order to allow for variations of the parameters with the redshift and scale, the first two parametrizations use recently suggested functional forms while the third is based on binning methods. Using the first parametrization, we find that the CMB + ISW + WL combination provides the strongest constraints on the MG parameters followed by CMB + WL or CMB + MPK + ISW. Using the second parametrization or the binning methods, we find that the combination CMB + MPK + ISW consistently provides some of the strongest constraints. This shows that the constraints are parametrization dependent. We find that adding up current data sets does not improve consistently the uncertainties on MG parameters due to tensions between the best-fit MG parameters preferred by different data sets. Furthermore, some functional forms imposed by the parametrizations can lead to an exacerbation of these tensions. Next, unlike some studies that used the CFHTLS lensing data, we do not find any deviation from general relativity using the refined HST-COSMOS data, confirming previous claims in those studies that their result may have been due to some systematic effect. Finally, for all the parametrizations and binning methods used, we find that the values corresponding to general relativity are within the 95% confidence level contours for all data set combinations.