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

We present constraints on the baryonic matter density parameter, ${\mathrm{\Omega }}_b$, within the framework of the $\mathrm{\Lambda }$CDM model. Our analysis utilizes observational data on the effective optical depth from high-redshift quasars. To parameterize the photoionization rate ${\mathrm{\Gamma }}_{-12}$, we employ a Bézier polynomial. Additionally, we approximate the Hubble parameter at high redshifts as $H(z)\approx 100h{\mathrm{\Omega }}_m^{1\mathrm{/}2}(1+z{)}^{3\mathrm{/}2}$ km s${}^{-1}$ Mpc${}^{-1}$. Confidence regions are obtained with $h=0.701\pm 0.013$ and ${\mathrm{\Omega }}_m=0.315$, optimized by the Planck mission. The best-fit values are ${\mathrm{\Omega }}_b=0.043_{-0.006}^{+0.005}$ and ${\mathrm{\Omega }}_b=0.045_{-0.006}^{+0.004}$, corresponding to an old data set and a new data set, respectively. And we test the non-parametric form of ${\mathrm{\Gamma }}_{-12}$, obtaining ${\mathrm{\Omega }}_b=0.048_{-0.003}^{+0.001}$. These results are consistent with the findings of Planck at the 1 $\sigma$ confidence level. Our findings underscore the effectiveness of quasar datasets in constraining ${\mathrm{\Omega }}_b$, 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.