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

The EG 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 EG 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 EG 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^GPlanck+CMASS=0.36-0.05+0.06(68.27%) and E^GPlanck+LOWZ=0.40-0.09+0.11(68.27%), with additional subdominant systematic error budget estimates of 2% and 3%, respectively. Using ωm,0 constraints from Planck and SDSS BAO observations, ΛCDM-GR predicts EGGR(z=0.555)=0.401±0.005 and EGGR(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 EG. This work provides a carefully constructed and calibrated statistic with which EG measurements can be confidently and accurately obtained with upcoming survey data.