Impact of lensing bias on the cosmological dispersion measure

TL;DR

This paper quantifies how gravitational lensing bias affects the measurement of cosmological dispersion measure from FRBs, showing a small but significant bias that must be accounted for in precision cosmology.

Contribution

It derives the lensing bias on the ensemble average DM from FRBs using cosmological perturbation theory and simulations, highlighting its importance for accurate cosmological inferences.

Findings

Lensing bias causes a 0.4%–1% reduction in average DM at z=1.

Lensing deflection leads to light rays avoiding high-density regions.

Magnification bias affects the observed DM distribution.

Abstract

The cosmological dispersion measure (DM) as a function of redshift, derived from localized fast radio bursts (FRBs), has been used as a tool for constraining the cosmic ionized fraction and cosmological parameters. For these purposes, the DM in a homogeneous cosmological model has typically been used, neglecting the inhomogeneity of matter distribution. In this study, we derive a bias in the ensemble average of the DM over many FRBs owing to gravitational lensing by the inhomogeneous matter distribution based on cosmological perturbation theory. We demonstrate that the ensemble average is $0.4 \, \%$--$1\,\%$ smaller than the DM in the corresponding homogeneous model for a source redshift of $z_{\rm s}=1$, according to recent cosmological hydrodynamic simulations of IllustrisTNG and BAHAMAS. This reduction occurs because light rays from FRBs tend to avoid high-density regions owing to lensing deflection. We also discuss another selection effect, magnification bias, where demagnified FRBs with low DMs, fainter than the detection threshold, are excluded from the observed sample, leading to a selective observation of magnified FRBs with high DMs. Lensing bias, including magnification bias, must be considered to achieve percent level accuracy in the DM--redshift relation.