Atacama Cosmology Telescope: DR6 gravitational lensing and SDSS BOSS cross-correlation measurement and constraints on gravity with the 𝐸 𝐺 statistic
We derive new constraints on the 𝐸 𝐺 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 𝐸 𝐺 statistic can distinguish Λ CDM from alternative models of gravity. We find 𝐸 𝐺 (𝑧 eff = 0.555) = 0.31$^{+0.06}_{−0.05}$ for Atacama Cosmology Telescope (ACT) and CMASS data at 68.28% confidence level, and 𝐸 𝐺 (𝑧 eff = 0.316) = 0.49$^{+0.14}_{−0.11}$ for the ACT and LOWZ. Systematic errors are estimated to be 3% and 4%, respectively. Including CMB lensing information from Planck PR4 results in 𝐸 𝐺 (𝑧 eff = 0.555) = 0.34$^{+0.05}_{−0.05}$ with CMASS and 𝐸 𝐺 (𝑧 eff = 0.316) = 0.43$^{+0.11}_{−0.09}$ with LOWZ. These are consistent with predictions for the Λ CDM model that best fits the Planck CMB anisotropy and SDSS BOSS baryon acoustic oscillations (BAO), where 𝐸$^{GR}_{𝐺}$(𝑧 eff =0.555) =0.401 ± 0.005 for CMB lensing combined with CMASS and 𝐸$^{GR}_{𝐺}$(𝑧 eff = 0.316) = 0.452 ± 0.005 combined with LOWZ. We also find 𝐸 𝐺 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.