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

Abstract

We present constraints on the baryonic matter density parameter, $Ω_b$, within the framework of the $Λ$CDM 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 $H(z)\approx 100hΩ_m^{1/2} (1+z)^{3/2}$ km s$^{-1}$ Mpc$^{-1}$. Confidence regions are obtained with $h=0.701\pm0.013$ and $Ω_m = 0.315$, optimized by the Planck mission. The best-fit values are $Ω_b =0.043^{+0.005}_{-0.006}$ and $Ω_b = 0.045^{+0.004}_{-0.006}$, corresponding to an old data set and a new data set, respectively. And we test the non-parametric form of $Γ_{-12}$, obtaining $Ω_b = 0.048^{+0.001}_{-0.003}$. These results are consistent with the findings of Planck at the 1 $σ$ confidence level. Our findings underscore the effectiveness of quasar datasets 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.