Fast radio burst dispersion is an unbiased tracer of matter on large scales

Abstract

The dispersion of fast radio bursts (FRBs) measures the column density of free electrons, tracing the diffuse ionized gas that contains more than $90\%$ of all baryons. On linear scales the FRB dispersion field is an approximately unbiased tracer of the matter distribution, an idea long assumed in the FRB large-scale structure literature and recently formalized by Zhou and Zhang [arXiv:2510.11022]. This follows from baryon-mass conservation, which forces the total baryon field to have unit linear bias, with dispersion inheriting this bias up to small corrections from the stellar and neutral-gas components. We show these corrections can be bounded at the percent level using existing galaxy and 21 cm surveys, and confirm with the FLAMINGO hydrodynamical simulations that the electron bias varies at the percent level across a wide range of feedback prescriptions. The dispersion-galaxy cross-power spectrum at linear scales directly constrains $B_8 \equiv \sigma_8(\Omega_b/0.05)^{1/2}$, a baryonic analog of $S_8$, independently of feedback physics. Because most of the per-object variance in dispersion is cosmological signal rather than noise, $\sim\!10^5$ localized FRBs can match the statistical power of $\sim\!10^8$ weak-lensing galaxy shape measurements. FRB dispersion thus joins weak lensing and redshift-space distortions as a new unbiased tracer of matter on large scales.