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

Abstract

We use cosmological constraints from current datasets and a figure of merit approach (FoM) in order to probe any deviations from general relativity at cosmological scales. The FoM approach is used to study and compare the constraining power of various combinations of datasets 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 LRG galaxy surveys, the matterpower spectrum from SDSS-DR7 (MPK), the WMAP7 temperature and polarization spectra, the BAO from 2DF 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 parameterizations 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 parameterizations use recently suggested functional forms while the third is based on binning methods. Using the first parameterization, 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 parameterization 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 parameterization dependent. We find that adding up current datasets does not improve consistently the uncertainties on MG parameters due to tensions between the best fit MG parameters preferred by different datasets. Furthermore, some functional forms imposed by the parameterizations 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 GR 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 parameterizations 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.

Constraints and tensions in testing general relativity from Planck and CFHTLenS data including intrinsic alignment systematics

“…We refer the reader to Refs. [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. A summary of the relationships among the various parametrizations can be found in [44].…”

“…It is a useful probe in that the galaxy distribution is sensitive to changes to the actual Poisson equation which probes changes in the parameter combination 2Σ − Q, while the ISW effect directly relates to the time derivative of the sum of the metric potentials and thus probes Σ and _ Σ. This likelihood and its usefulness in testing for deviations from general relativity has been discussed extensively in previous works, for example, [25,[41][42][43][44]46]. As a final probe of the matter distribution of the Universe we use the weak-lensing tomography shear-shear crosscorrelation data.…”

Figure of merit and different combinations of observational data sets

“…errors will be given, which are obtained by using the Markov chain Monte Carlo method. To estimate and compare the goodness of constraints from the observational data sets, we calculate the FoM [40][41][42]46] for each combination of data sets, which is proportional to the inverse area of the error ellipse in the w 0 $ w 1 plane:…”

“…The fitting properties of observational data will be studied by using the Dark Energy Task Force [40][41][42] fiducial model (CPL model); i.e., all combinations of data will be fitted with the CPL parametrization. The best-fitted values of m0 , w 0 , w 1 and their 68%, 95% C.L.…”

“…errors for each combination will be given. To estimate constraints on w de and compare the goodness of data, we will calculate the figure of merit (FoM) [40][41][42] for each combination, which is proportional to the inverse area of the error ellipse in the w 0 $ w 1 plane. Namely, we will take the FoM as the diagnostic to quantify the goodness of each combination of observational data to constrain the DE parameters.…”