Testing General Relativity on cosmological scales at redshift z ~ 1.5
  with quasar and CMB lensing
  We test general relativity (GR) at the effective redshift $\bar{z} \sim 1.5$
by estimating the statistic $E_G$, a probe of gravity, on cosmological scales
$19 - 190\,h^{-1}{\rm Mpc}$. This is the highest-redshift and largest-scale
estimation of $E_G$ so far. We use the quasar sample with redshifts $0.8 < z <
2.2$ from Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic
Survey (eBOSS) Data Release 16 (DR16) as the large-scale structure (LSS)
tracer, for which the angular power spectrum $C_\ell^{qq}$ and the
redshift-space distortion (RSD) parameter $\beta$ are estimated. By cross
correlating with the $\textit{Planck}$ 2018 cosmic microwave background (CMB)
lensing map, we detect the angular cross-power spectrum $C_\ell^{\kappa q}$
signal at $12\,\sigma$ significance. Both jackknife resampling and simulations
are used to estimate the covariance matrix (CM) of $E_G$ at $5$ bins covering
different scales, with the later preferred for its better constraints on the
covariances. We find $E_G$ estimates agree with the GR prediction at
$1\,\sigma$ level over all these scales. With the CM estimated with $300$
simulations, we report a best-fit scale-averaged estimate of
$E_G(\bar{z})=0.30\pm 0.05$, which is in line with the GR prediction $E_G^{\rm
GR}(\bar{z})=0.33$ with $\textit{Planck}$ 2018 CMB+BAO matter density fraction
$\Omega_{\rm m}=0.31$. The statistical errors of $E_G$ with future LSS surveys
at similar redshifts will be reduced by an order of magnitude, which makes it
possible to constrain modified gravity models.
