Measuring the density of the intergalactic medium using quasar sight lines in the epoch of reionization is challenging due to the saturation of Lyα absorption. Near a luminous quasar, however, the enhanced radiation creates a proximity zone observable in the quasar spectra where the Lyα absorption is not saturated. In this study, we use 10 high-resolution (R ≳ 10,000) z ~ 6 quasar spectra from the extended XQR-30 sample to measure the density field in the quasar proximity zones. We find a variety of environments within 3 pMpc distance from the quasars. We compare the observed density cumulative distribution function (CDF) with models from the Cosmic Reionization on Computers simulation and find a good agreement between 1.5 and 3 pMpc from the quasar. This region is far away from the quasar hosts and hence approaching the mean density of the universe, which allows us to use the CDF to set constraints on the cosmological parameter σ 8 = 0.6 ± 0.3. The uncertainty is mainly due to the limited number of high-quality quasar sight lines currently available. Utilizing the more than 200 known quasars at z ≳ 6, this method will allow us to tighten the constraint on σ 8 to the percent level in the future. In the region closer to the quasar within 1.5 pMpc, we find that the density is higher than predicted in the simulation by 1.23 ± 0.17, suggesting that the typical host dark matter halo mass of a bright quasar (M 1450 < -26.5) at z ~ 6 is log10(Mh/M⊙)=12.5+0.4−0.7.
