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

TL;DR

FRBs provide a cosmological probe through the extragalactic dispersion measure $\mathrm{DM}_{\mathrm{exgal}}$ as a function of redshift $z$, but survey selection effects and FRB population evolution can bias inference if not properly accounted. The authors build forward-model FRB populations and a neural-network emulator for the variance $\sigma^2[\mathrm{DM}_{\mathrm{cosmic}}(z)]$, enabling fast likelihood evaluations for $p(\mathrm{DM}_{\mathrm{exgal}}|z)$. Their key finding is that current samples yield robust conditional inferences with biases $\lesssim 0.8\sigma$ for $10^2$ FRBs and $\lesssim 3\sigma$ for $10^4$ FRBs only if selection effects are modeled; without modeling, biases can become substantial in the large-sample regime. They also show that high-redshift FRBs tighten constraints on $\sigma_8$ and the baryonic feedback parameter $\log M_c$, while low-redshift FRBs better constrain the host DM distribution, underscoring the value of a broad redshift coverage for robust FRB-based cosmology.

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, $σ^2[\mathrm{DM}_{\mathrm{cosmic}}(z)]$, 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 $\lesssim0.8σ$ 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 $3σ$ for $10^4$ FRBs, thus implying that explicit modeling of selection effects will be essential for next-generation samples.

Figures (4)

• Figure 1: Accuracy of the emulator for FRB dispersion measure variance, $\sigma [\mathrm{DM}_\mathrm{cosmic}]$ as a function of redshift $z$, under the halo model prescription 2024OJAp....7E.108A with baryonification halo gas profiles 2015JCAP...12..049S2019JCAP...03..020S. We show the 68%, 95% and 99% upper limits on the distribution of error in emulated variance compared to the true variance. We achieve $\leq$4% accuracy up to redshift 4 on validation dataset.
• Figure 2: Quantifying the impact of population redshift evolution and luminosity function on cosmological parameter inference conducted using $p(\mathrm{DM}_\mathrm{exgal}|z)$. Top panel illustrates the impact of FRB redshift distribution (controlled by $z_\ast$) on $p(\mathrm{DM}_\mathrm{cosmic}, z)$ (first row) and $p(\mathrm{DM}_\mathrm{cosmic} | z)$ (second row) distributions. The black lines indicate the 68% and 95% confidence intervals of $p(\mathrm{DM}_\mathrm{exgal}|z)$. Bottom panel quantifies the bias in inferred parameters, $b_p = (p-p^\mathrm{True})/p^\mathrm{True}$, for various FRB redshift distributions ($z_\ast$). The solid line indicates the inferred bias in no selection effects scenario, which is consistent with zero within $1\sigma$ (shaded region). The bias in parameters when inference is conducted using $p(\mathrm{DM}_\mathrm{exgal}|z)$ (without modeling any selection effects) is shown as stars and when the inference is conducted using $p(\mathrm{DM}_\mathrm{FRB}, z)$ (by modeling selection effects) is shown as squares. For a sample of $10^2$ FRBs (blue), without modeling selection effects, the bias in parameters is consistent with zero within $1\sigma$. As the constraining power increases with $10^4$ FRBs (yellow), the bias in parameters still remains $\lesssim 1\sigma$ when selection effects are not accounted. The bias remains $\lesssim 1\sigma$ after modeling the selection effects.
• Figure 3: Quantifying the impact of strict DM cuts on cosmological parameter inference conducted using $p(\mathrm{DM}_\mathrm{exgal}|z)$. Top panel illustrates the impact of DM$_\mathrm{cut}$ on $p(\mathrm{DM}_\mathrm{cosmic}, z)$ (first row) and $p(\mathrm{DM}_\mathrm{cosmic} | z)$ (second row) distributions. The black lines indicate the 68% and 95% confidence intervals of $p(\mathrm{DM}_\mathrm{exgal}|z)$. Bottom panel quantifies the bias in inferred parameters, $b_p = (p-p^\mathrm{True})/p^\mathrm{True}$, for various DM$_\mathrm{cut}$. The solid line indicates the inferred bias in no selection effects scenario, which is consistent with zero within $1\sigma$ (shaded region). The bias in parameters when inference is conducted using $p(\mathrm{DM}_\mathrm{exgal}|z)$ (without modeling any selection effects) is shown as stars and when the inference is conducted using $p(\mathrm{DM}_\mathrm{FRB}, z)$ (by modeling selection effects) is shown as squares. For a sample of $10^2$ FRBs (blue), without modeling selection effects, the bias in parameters is consistent with zero within $1\sigma$. As the constraining power increases with $10^4$ FRBs (yellow), the bias in parameters can be larger than $3\sigma$ if selection effects are not accounted. Modeling selection effects removes this bias.
• Figure 4: Quantifying the impact of the strength of DM cut on cosmological parameter inference conducted using $p(\mathrm{DM}_\mathrm{exgal}|z)$. Top panel illustrates the impact of DM$_\mathrm{cut}$ strength (denoted by $s$) on $p(\mathrm{DM}_\mathrm{cosmic}, z)$ (first row) and $p(\mathrm{DM}_\mathrm{cosmic} | z)$ (second row) distributions. The black lines indicate the 68% and 95% confidence intervals of $p(\mathrm{DM}_\mathrm{exgal}|z)$. Bottom panel quantifies the bias in inferred parameters, $b_p = (p-p^\mathrm{True})/p^\mathrm{True}$, for various DM$_\mathrm{cut}$. The solid line indicates the inferred bias in no selection effects scenario, which is consistent with zero within $1\sigma$ (shaded region). The bias in parameters when inference is conducted using $p(\mathrm{DM}_\mathrm{exgal}|z)$ (without modeling any selection effects) is shown as stars and when the inference is conducted using $p(\mathrm{DM}_\mathrm{FRB}, z)$ (by modeling selection effects) is shown as squares. For a sample of $10^2$ FRBs (blue), without modeling selection effects, the bias in parameters is consistent with zero within $1\sigma$. As the constraining power increases with $10^4$ FRBs (yellow), the bias in parameters can be larger than $1\sigma$ if selection effects are not accounted. Modeling selection effects removes this bias and the loss in constraining power from additional parameters is negligible.