Probing gravity with a joint analysis of galaxy and CMB lensing and SDSS
  spectroscopy
  We present measurements of $E_G$, a probe of gravity from large-scale
structure, using BOSS LOWZ and CMASS spectroscopic samples, with lensing
measurements from SDSS (galaxy lensing) and Planck (CMB lensing). Using SDSS
lensing and the BOSS LOWZ sample, we measure
$\langle{E_G}\rangle=0.40^{+0.05}_{-0.04}$ (stat), $\pm 0.026$ (systematic),
consistent with the predicted value from the Planck $\Lambda$CDM model,
$E_G=0.46$. Using CMB lensing, we measure
$\langle{E_G}\rangle=0.46^{+0.08}_{-0.09}$ (stat) for LOWZ (statistically
consistent with galaxy lensing and Planck predictions) and
$\langle{E_G}\rangle=0.39^{+0.05}_{-0.05}$ (stat) for the CMASS sample,
consistent with the Planck prediction of $E_G=0.40$ given the higher redshift
of the sample. We also study the redshift evolution of $E_G$ by splitting the
LOWZ sample into two samples based on redshift, with results being consistent
with model predictions. We estimate systematic uncertainties on the above
$\langle{E_G}\rangle$ numbers to be $\sim 6$% (when using galaxy-galaxy
lensing) or $\sim 3$% (when using CMB lensing), subdominant to the quoted
statistical errors. These systematic error budgets are dominated by
observational systematics in galaxy-galaxy lensing and by theoretical modeling
uncertainties, respectively. We do not estimate observational systematics in
galaxy-CMB lensing cross correlations.
