Constraints on the Helium Abundance from Fast Radio Bursts

TL;DR

This study explores how fast radio bursts (FRBs) can be used to measure the universe's helium abundance, demonstrating improved constraints with larger, high-redshift FRB samples and prior cosmological data.

Contribution

It introduces a method to constrain helium abundance using FRB dispersion measures, incorporating Planck priors, and forecasts improved accuracy with future high-redshift FRB data.

Findings

Current low-redshift FRB data cannot tightly constrain helium abundance.

Simulated data suggests a standard deviation of 0.025 for $Y_{He}$ with 500 FRBs.

High-redshift FRB data could improve the constraint to a standard deviation of 0.011.

Abstract

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.