Constraining Gravity at the Largest Scales through CMB Lensing and Galaxy Velocities

Abstract: 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 $\sigma_8$. While traditionally, the lensing field for $E_G$ 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/$h$, 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 $\beta$. We report $E_G(z=0.57)=0.243\pm0.060$ (stat) $\pm0.013$ (sys), a measurement in tension with the general relativity prediction at a level of 2.6$\sigma$. Note that our $E_G$ measurement deviates from GR only at scales greater than 80 Mpc/$h$, 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.