Probing the Bias of Large-Scale Structure with Unlocalized Fast Radio Bursts

Abstract

Large-scale structure (LSS) and tracer bias connect observable populations to the cosmic matter distribution. While galaxies are standard tracers, transient events such as gravitational-wave sources can also probe LSS despite large localization uncertainties. Fast radio bursts (FRBs), owing to their cosmological distances and dispersion-measure information, provide a promising complementary tracer of LSS. However, most FRBs lack precise localization and redshift measurements, introducing severe angular and radial errors that dilute the clustering signal. Here we construct an end-to-end framework to infer the linear large-scale bias of unlocalized FRB populations using the isotropic two-point correlation function. Our pipeline adopts the Landy-Szalay estimator with noise-matched random catalogs, a Monte Carlo forward model accounting for localization smearing, and likelihood-based inference with covariance matrices from lognormal mock samples. We test the method on synthetic FRB samples at redshifts z=0.3, 0.5, and 0.7 with injected bias values b=1.2, 1.5, and 2.0. The measured correlation functions closely follow smeared theoretical predictions, confirming that positional uncertainty dominates clustering suppression. Despite sample variance, the inferred bias posteriors recover the true inputs and preserve relative bias ordering. Discrimination is strongest at low redshift and weakens at higher redshift, where low-bias populations become poorly constrained. Our results demonstrate that meaningful large-scale clustering information can be extracted from poorly localized FRBs when smearing effects are properly modeled, establishing a practical route for future FRB-based LSS investigations.

Figures (3)

• Figure 1: Representative recovery of the localization-smeared two-point correlation function for the mock sample with $z=0.3$ and $b_{\rm inj}=1.2$. The dotted black curve shows the unsmeared theoretical prediction, and the solid black curve shows the smeared prediction after convolving with the adopted localization kernel. Thin colored curves denote the individual measurements from 1000 realizations; the red solid and blue dashed curves mark the ensemble mean and median, respectively. The dark and light gray shaded regions indicate the $1\sigma$ and $3\sigma$ ranges.
• Figure 2: Recovered FRB bias as a function of redshift for three injected values, $b_{\rm inj}=1.2$, $1.5$, and $2.0$ (from left to right). The dashed horizontal line in each panel marks the injected bias. Points with vertical error bars show the recovered posterior central value and the corresponding $68\%$ credible interval in each redshift bin. The overall trend indicates that the constraining power weakens toward higher redshift, especially for the lowest-bias case.
• Figure 3: Stacked posterior densities of the FRB bias parameter $b$ in the three redshift bins $z=0.3$, $0.5$, and $0.7$. Blue, orange, and green correspond to injected biases $b_{\rm inj}=1.2$, $1.5$, and $2.0$, respectively. Thick curves denote the stacked posterior densities, thin curves show the posteriors from individual realizations, semi-transparent histograms indicate the best-fit-density distribution, and vertical dashed lines mark the injected values. The separation between the three bias cases is clearest at low redshift and weakens toward $z=0.7$, especially for the lowest-bias sample.