The completed SDSS-IV extended baryon oscillation spectroscopic survey: Geometry and growth from the anisotropic void-galaxy correlation function in the luminous red galaxy sample

We present an analysis of the anisotropic redshift-space void-galaxy correlation in configuration space using the Sloan Digital Sky Survey extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 luminous red galaxy (LRG) sample. This sample consists of LRGs between redshifts 0.6 and 1.0, combined with the high redshift z > 0.6 tail of the Baryon Oscillation Spectroscopic Survey Data Release 12 CMASS sample. We use a reconstruction method to undo redshift-space distortion (RSD) effects from the galaxy field before applying a watershed void-finding algorithm to remove bias from the void selection. We then perform a joint fit to the multipole moments of the correlation function for the growth rate fσ ₈ and the geometrical distance ratio D_M/D_H, finding f σ₈ (z_eff ) = 0.356 ± 0.079 and D_M /D_H (z_eff ) = 0.868 ± 0.017 at the effective redshift zeff = 0.69 of the sample. The posterior parameter degeneracies are orthogonal to those from galaxy clustering analyses applied to the same data, and the constraint achieved on D_M/D_H is significantly tighter. In combination with the consensus galaxy BAO and full-shape analyses of the same sample, we obtain fσ ₈ = 0.447 ± 0.039, D_M/r_d = 17.48 ± 0.23, and D_H/r_d = 20.10 ± 0.34. These values are in good agreement with the ΛCDM model predictions and represent reductions in the uncertainties of 13 per cent, 23 per cent, and 28 per cent, respectively, compared to the combined results from galaxy clustering, or an overall reduction of 55 per cent in the allowed volume of parameter space.