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 (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.

Automated summary

The study tests gravity at high redshift and large scales, finding that general relativity predictions hold true at various scales. The use of a large sample size and simulations for validation has potential for constraining modified gravity models in the future.