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 $\sigma_8$. 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.
