Constraints on Baryon Density from the Effective Optical Depth of High-redshift Quasars

We present constraints on the baryonic matter density parameter, Ω b , within the framework of the ΛCDM model. Our analysis utilizes observational data on the effective optical depth from high-redshift quasars. To parameterize the photoionization rate Γ −12 , we employ a Bézier polynomial. Additionally, we approximate the Hubble parameter at high redshifts as H ( z ) ≈ 100 h Ω m 1 / 2 ( 1 + z ) 3 / 2 km s −1 Mpc −1 . Confidence regions are obtained with h = 0.701 ± 0.013 and Ω m = 0.315, optimized by the Planck mission. The best-fit values are Ω b = 0.04 3 − 0.006 + 0.005 and Ω b = 0.04 5 − 0.006 + 0.004 , corresponding to an old data set and a new data set, respectively. We test the non-parametric form of Γ −12 , obtaining Ω b = 0.04 8 − 0.003 + 0.001 . These results are consistent with the findings of Planck at the 1 σ confidence level. Our findings underscore the effectiveness of quasar data sets in constraining Ω b , eliminating the need for independent photoionization rate data. This approach provides detailed cosmic information about baryon density and the photoionization history of the intergalactic medium.