Constraints on the Helium Abundance from Fast Radio Bursts

Through the relationship between dispersion measures (DM) and redshifts, fast radio bursts (FRBs) are considered to be very promising cosmological probes. In this paper, we attempted to use the DM-z relationship of FRBs to study the helium abundance ($Y_{\rm He}$) in the universe. First, we used 17 current FRBs with known redshifts for our study. Due to their low redshifts and the strong degeneracy between $Y_{\rm He}$ and $\Omega_bh^2$, however, this catalog could not provide a good constraint on the helium abundance. Then, we simulated 500 low redshift FRB mock data with $z\in[0,\,1.5]$ to forecast the constraining ability on $Y_{\rm He}$. In order to break the degeneracy between $Y_{\rm He}$ and $\Omega_bh^2$ further, we introduced the shift parameters of the Planck measurement $(R,l_A,\Omega_bh^2)$ as a prior, where $\Omega_bh^2$ represents the baryon density parameter, and $R$ and $l_A$ correspond to the scaled distance to recombination and the angular scale of the sound horizon at recombination, respectively. We obtained the standard deviation for the helium abundance: $\sigma({Y_{\rm He}}) = 0.025$. Finally, we considered 2000 higher redshift FRB data with the redshift distribution of $[0,\,3]$ and found that the constraining power for $Y_{\rm He}$ would be improved by more than 2 times, $\sigma({Y_{\rm He}}) = 0.011$, which indicates that the FRB data with high redshift can provide a better constraint on the helium abundance. Hopefully, large FRB samples with high redshift from the Square Kilometre Array can provide high-precision measurements of the helium abundance in the near future.