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 data sets and a figure of merit (FoM) approach to probe any deviations from general relativity (GR) at cosmological scales. The FoM approach is used to study the constraining power of various combinations of data sets on modified gravity (MG) parameters. We use recently refined HST-COSMOS weak-lensing tomography data, ISW-galaxy cross correlations from 2MASS and SDSS LRG surveys, matter power spectrum from SDSS-DR7 (MPK), WMAP7 temperature and polarization spectra, BAO from 2DF and SDSS-DR7, and Union2 compilation of supernovae, in addition to other bounds from H_0 measurements and BBN. We use 3 parametrizations of MG parameters that enter the perturbed field equations. In order to allow for variations with redshift and scale, the first 2 parametrizations use recently suggested functional forms while the third is based on binning methods. Using the first parametrization, we find that CMB + ISW + WL provides the strongest constraints on MG parameters followed by CMB+WL or CMB+MPK+ISW. Using the second parametrization or binning methods, 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 uncertainties on MG parameters due to tensions between 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 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, we find in all cases that the values corresponding to GR are within the 95% confidence level contours for all data set combinations. (abridged)

18 pages, 6 figures, matches version published in PRD

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• Cluster Density Profiles as a Test of Modified Gravity
• The Paths of Gravity in Galileon Cosmology
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• Cosmological discordances II: Hubble constant, Planck and large-scale-structure data sets
• Constraining models of $f(R)$ gravity with Planck and WiggleZ power spectrum data
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• Prospects of strongly lensed repeating fast radio bursts: complementary constraints on dark energy evolution
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• Cosmological discordances III: more on measure properties, Large-Scale-Structure constraints, the Hubble constant and Planck
• Separating the Intrinsic Alignment Signal and the Lensing Signal using Self-Calibration in Photo-z Surveys with KiDS450 and KV450 Data
• ISiTGR: Testing deviations from GR at cosmological scales including dynamical dark energy, massive neutrinos, functional or binned parametrizations, and spatial curvature
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• Figure of Merit and Different Combinations of Observational Data Sets
• Singling out modified gravity parameters and datasets reveals a dichotomy between Planck and lensing
• Constraining Scale Dependent Growth with Redshift Surveys