Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the EG statistic

We derive new constraints on the EG statistic as a test of gravity, combining the cosmic microwave background (CMB) lensing map estimated from Data Release 6 (DR6) of the Atacama Cosmology Telescope with Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (SDSS BOSS) CMASS and LOWZ galaxy data. We develop an analysis pipeline to measure the cross-correlation between CMB lensing maps and galaxy data, following a blinding policy and testing the approach through null and consistency checks. By testing the equivalence of the spatial and temporal gravitational potentials, the EG statistic can distinguish Lambda CDM from alternative models of gravity. We find EG(zeff = 0.555) = 0.31 & thorn;0.06 -0.05 for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and EG(zeff = 0.316) = 0.49 & thorn;0.14 -0.11 for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in EG(zeff = 0.555) = 0.34 & thorn;0.05 -0.05 with CMASS and EG(zeff = 0.316) = 0.43 & thorn;0.11 -0.09 with LOWZ. These are consistent with predictions for the ACDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where EGR G (zeff = 0.555) = 0.401 + 0.005 for CMB lensing combined with CMASS and EGR G (zeff = 0.316) = 0.452+0.005 combined with LOWZ. We also find EG to be scale independent, with probability to exceed > 5%, as predicted by general relativity. The methods developed in this work are also applicable to improved future analyses with upcoming spectroscopic galaxy samples and CMB lensing measurements.