Testing general relativity on cosmological scales at redshift z similar to 1.5 with quasar and CMB lensing

We test general relativity (GR) at the effective redshift (z) over tilde similar to 1.5 by estimating the statistic E-G, a probe of gravity, on cosmological scales 19 - 190 h(-1)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 Data Release 16 as the large-scale structure (LSS) tracer, for which the angular power spectrum C-l(qq) and the redshift-space distortion parameter beta are estimated. By cross-correlating with the Planck 2018 cosmic microwave background (CMB) lensing map, we detect the angular cross-power spectrum Cl-kappa q signal at 12 sigma significance. Both jackknife resampling and simulations are used to estimate the covariance matrix (CM) of E-G at five 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-fitting scale-averaged estimate of E-G((z) over bar) = 0.30 +/- 0.05, which is in line with the GR prediction E-G(GR)((z) over bar) = 0.33 with Planck 2018 CMB + BAO matter density fraction Omega(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.