Constraining gravity at the largest scales through CMB lensing and galaxy velocities

We demonstrate a new method to constrain gravity on the largest cosmological scales by combining measurements of cosmic microwave background (CMB) lensing and the galaxy velocity field. EG is a statistic, constructed from a gravitational lensing tracer and a measure of velocities such as redshift-space distortions (RSD), that can discriminate between gravity models while being independent of clustering bias and σ8. While traditionally, the lensing field for EG has been probed through galaxy lensing, CMB lensing has been proposed as a more robust tracer of the lensing field for EG at higher redshifts while avoiding intrinsic alignments. We perform the largest-scale measurement of EG ever, up to 150 Mpc h−1, by cross-correlating the Planck CMB lensing map with the Sloan Digital Sky Survey III (SDSS-III) CMASS galaxy sample and combining this with our measurement of the CMASS auto-power spectrum and the RSD parameter β. We report EG(z = 0.57) = 0.243 ± 0.060 (stat) ± 0.013 (sys), a measurement in tension with the general relativity (GR) prediction at a level of 2.6σ. Note that our EG measurement deviates from GR only at scales greater than 80 Mpc h−1, scales which have not been probed by previous EG tests. Upcoming surveys, which will provide an order-of-magnitude reduction in statistical errors, can significantly constrain alternative gravity models when combined with better control of systematics.