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. E_G 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 E_G at higher redshifts while avoiding intrinsic alignments. We perform the largest-scale measurement of E_G 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 E_G(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 E_G measurement deviates from GR only at scales greater than 80 Mpc h⁻¹, scales which have not been probed by previous E_G 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.