Testing gravity on large scales by combining weak lensing with galaxy clustering using CFHTLenS and BOSS CMASS

Abstract: We measure a combination of gravitational lensing, galaxy clustering, and redshift-space distortions called $E_G$. The quantity $E_G$ probes both parts of metric potential and is insensitive to galaxy bias and $\sigma_8$. These properties make it an attractive statistic to test $\Lambda$CDM, General Relativity and its alternate theories. We have combined CMASS DR11 with CFHTLenS and recent measurements of $\beta$ from RSD analysis, and find $E_G(z = 0.57) = 0.42 \pm 0.056$, an 13\% measurement in agreement with the prediction of general relativity $E_G(z = 0.57) = 0.396 \pm 0.011$ using the Planck 2015 cosmological parameters. We have corrected our measurement for various observational and theoretical systematics. Our measurement is consistent with the first measurement of $E_G$ using CMB lensing in place of galaxy lensing (Pullen et. al. 2015a) at small scales, but shows 2.8$\sigma$ tension when compared with their final results including large scales. This analysis with future surveys will provide improved statistical error and better control over systematics to test General Relativity and its alternate theories.