2025RAA....25b5021L

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 $H(z)\approx 100h{\Omega }_{m}^{1/2}{(1+z)}^{3/2}$ 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 ${\Omega }_{b}=0.04{3}_{-0.006}^{+0.005}$ and ${\Omega }_{b}=0.04{5}_{-0.006}^{+0.004}$, corresponding to an old data set and a new data set, respectively. We test the non-parametric form of Γ_–12, obtaining ${\Omega }_{b}=0.04{8}_{-0.003}^{+0.001}$. These results are consistent with the findings of Planck at the 1σ 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.