Constraining gravity with a new precision E_G estimator using Planck + SDSS BOSS

The E_G statistic is a discriminating probe of gravity developed to test the prediction of general relativity (GR) for the relation between gravitational potential and clustering on the largest scales in the observable universe. We present a novel high-precision estimator for the E_G statistic using CMB lensing and galaxy clustering correlations that carefully matches the effective redshifts across the different measurement components to minimize corrections. A suite of detailed tests is performed to characterize the estimator's accuracy, its sensitivity to assumptions and analysis choices and the non-Gaussianity of the estimator's uncertainty is characterized. After finalization of the estimator, it is applied to Planck CMB lensing and SDSS CMASS and LOWZ galaxy data. We report the first harmonic space measurement of E_G using the LOWZ sample and CMB lensing and also updated constraints using the final CMASS sample and the latest Planck CMB lensing map. We find E_G^Planck+CMASS = 0.36^+0.06_-0.05 (68.27 E_G^Planck+LOWZ = 0.40^+0.11_-0.09 (68.27 additional subdominant systematic error budget estimates of 2 respectively. Using Ω_ m,0 constraints from Planck and SDSS BAO observations, ΛCDM-GR predicts E_G^ GR (z = 0.555) = 0.401 ± 0.005 and E_G^ GR (z = 0.316) = 0.452 ± 0.005 at the effective redshifts of the CMASS and LOWZ based measurements. We report the measurement to be in good statistical agreement with the ΛCDM-GR prediction, and report that the measurement is also consistent with the more general GR prediction of scale-independence for E_G. This work provides a carefully constructed and calibrated statistic with which E_G measurements can be confidently and accurately obtained with upcoming survey data.