Quantifying the impact of selection effects on FRB DM-$z$ relation cosmological inference

Abstract

Fast Radio Bursts (FRBs) have emerged as powerful probes of baryonic matter in the Universe, offering constraints on cosmological and feedback parameters through their extragalactic dispersion measure-redshift (DM$_\mathrm{exgal}$-$z$) relation. However, the observed FRB population is shaped by complex selection effects arising from instrument sensitivity, DM-dependent search efficiency, and FRB source population redshift-evolution. In this work, we quantify the impact of such observational and population selection effects on cosmological inference derived from the conditional distribution $p(\mathrm{DM}_{\mathrm{exgal}}|z)$. Using forward-modeled FRB population simulations, we explore progressively realistic survey scenarios incorporating redshift evolution, luminosity function, and instrument DM selection function. To enable rapid likelihood evaluations, we build a neural-network emulator for the variance in cosmic DM, $\sigma^2[\mathrm{DM}_{\mathrm{cosmic}}(z)]$, trained on $5\times10^4$ baryonification halo-model simulations, achieving $\leq4\%$ accuracy up to $z=4$. We demonstrate that while redshift and DM-dependent selection effects substantially alter the joint distribution $p(\mathrm{DM},z)$, they have a negligible impact on the conditional distribution $p(\mathrm{DM}_{\mathrm{exgal}}|z)$ for current sample sizes. The parameter biases are $\lesssim0.8\sigma$ for $10^2$ FRBs, indicating that conditional analyses are robust for present surveys. However, depending on the survey DM-dependent search efficiency, these biases may exceed $3\sigma$ for $10^4$ FRBs, thus implying that explicit modeling of selection effects will be essential for next-generation samples.