A bayesian determination of the Hubble constant using 126 fast radio bursts

1 Introduction

Fast radio bursts (FRBs) are short transients in radio waves whose astrophysical origin remains unknown (Lorimer et al., 2007; Petroff et al., 2019; Lorimer et al., 2024). These exceptionally energetic phenomena have been detected at frequencies ranging from hundreds of MHz to several GHz. Their Dispersion Measure (DM) exceeds the galactic value, so they are essentially extragalactic events (Thornton et al., 2013), with the notable exception of FRB 20200428A, whose origin is confirmed from the Galactic magnetar SGR 1935 + 2154. Since their first detection in 2007 (Lorimer et al., 2007), more than 800 distinct FRBs have been detected (Collaboration et al., 2026; Xu et al., 2023). Most of them are unique events (non-repeating) or have not yet been observed to repeat (Beniamini and Kumar, 2025), although some repeating events have been characterized and classified based on their similarity to FRB 20121102 and FRB 20180916.

The main observable in the study of these transients is the observed Dispersion Measure ( DM obs ). This quantity corresponds to the integral of the free-electron density along the path followed by the signal. It is also related to the time delay between the signal’s highest and lowest frequencies. Each environment through which the signal passes contributes to the DM (Pol et al., 2019; Zhang et al., 2020; Zhu and Feng, 2021): the Milky Way, through its halo ( DM MW, halo ) and interstellar medium ( DM MW, ISM ); DM IGM, including the diffuse intergalactic medium and the halos of galaxy clusters, groups, and galaxies (Connor et al., 2024); and the host-galaxy environment ( DM host ). In particular, DM IGM makes this quantity sensitive to H 0.

Recent studies have focused on modeling the connection between observed DM and the corresponding redshift z. For example, (Macquart et al., 2020; Cui et al., 2022; Baptista et al., 2023; Piratova-Moreno and García, 2024; Xu et al., 2021), have proposed different models for the DM–z relationship, including a linear trend, a log-parabolic relationship, a power-law model, and models that consider angular dependencies, not just those in z. By studying the cosmological contribution to the DM of FRBs, we can address cosmological questions, including the distribution of baryons in the Universe (Macquart et al., 2020; Yang et al., 2022), the parameters of the ΛCDM model, dark energy models (Deng and Zhang, 2014; Zheng et al., 2014) and one of the most challenging problems in modern cosmology: the Hubble Tension (Kalita et al., 2025; Acharya and Beniamini, 2025; Xu et al., 2025; Piratova-Moreno et al., 2025; Valentino et al., 2025; Di Valentino et al., 2021; Kamionkowski and Riess, 2023; Verde et al., 2024).

The Hubble Tension is the difference between early- and late-universe measurements of the Hubble constant H 0 with a significance level of approximately ∼ 5 σ. This difference is shown by the H 0 values inferred from the CMB: 67.4 ± 0.5km s − 1 Mpc − 1 (Planck et al., 2020), and a recent publication on SNIa: 73.0 ± 1.0km s − 1 Mpc − 1 (Riess et al., 2022), measured in the local Universe by the SH0ES collaboration. Several works have proposed ways to alleviate or even resolve the Hubble tension: revisiting local-distance-ladder systematics, including Cepheid color-luminosity calibration, metallicity, supernova magnitudes, and Gaia parallaxes, led to a reported value of H 0 = 68.1 ± 2.6 k m s − 1 M p c − 1, removing the tension with the Planck value in that analysis (Mörtsell et al., 2022); updated TRGB calibrations applied to Type Ia supernovae yielded H 0 = 69.8 ± 0.6 ( s t a t ) ± 1.6 ( s y s ) k m s − 1 M p c − 1, with no statistically significant difference with the CMB-based result (Freedman, 2021); early-dark-energy scenarios have identified regions of parameter space in which the H 0 inferred from Planck data agrees with the SH0ES local measurement (Poulin et al., 2019); and a new early-dark-energy model yielded H 0 = 69 . 6 − 1.3 + 1.0 k m s − 1 M p c − 1, reducing the tension to 2.5 σ (Niedermann and Sloth, 2020). Nevertheless, the origin of the Hubble tension remains unsettled and continues to motivate alternative probes. In this context, fast radio bursts (FRBs) provide a promising independent way to probe H 0, since their dispersion measure (DM) contains information about the cosmological distance to the source.

Several groups have used FRBs for measuring the Hubble constant using different methodologies and sample sizes, for instance: using Maximum Likelihood Estimation with 9 FRBs, a value of H 0 = 62.3 ± 9.1 km s − 1 Mpc − 1 was reported (Hagstotz et al., 2022), while an H 0 measurement derived from a Bayesian MCMC analysis of 18 localized FRBs yielded H 0 = 68.8 1 − 4.33 + 4.99 km s − 1 Mpc − 1 (Wu et al., 2022). A consistent value of H 0 = 71 ± 3 km s − 1 Mpc − 1 was found using a similar number of bursts (Liu et al., 2023). A Bayesian MCMC analysis of 95 localized FRBs yielded H 0 = 71.2 8 − 2.08 + 1.90 km s − 1 Mpc − 1 under ΛCDM, alongside a detailed assessment of systematic effects (Xu et al., 2025). Combining 12 unlocalized FRBs with BBN constraints led to H 0 = 80 . 4 − 19.4 + 24.1 km s − 1 Mpc − 1 (Zhao et al., 2022), while using temporal scattering effects from 30 FRBs gave H 0 = 7 4 − 7.2 + 7.5 km s − 1 Mpc − 1 (Yang et al., 2025). With intermediate sample sizes: an analysis of 16 FRBs yielded H 0 = 7 3 − 8 + 13 km s − 1 Mpc − 1 (James et al., 2022a), and using 26 FRBs from multiple surveys produced H 0 = 6 4 − 13 + 15 km s − 1 Mpc − 1 (Hoffmann et al., 2024). Applying Monte Carlo simulations to 69 localized FRBs gave H 0 = 70.4 1 − 2.34 + 2.28 km s − 1 Mpc − 1 (Gao et al., 2024), while 64 localized FRBs yielded H 0 = 83.5 3 − 2.32 + 2.92 km s − 1 Mpc − 1 (Kalita et al., 2025). An analysis of 78 FRBs yielded H 0 = 85 . 3 − 9.3 + 8.1 km s − 1 Mpc − 1 (Baptista et al., 2024). Using 92 localized FRBs in (Wang et al., 2025) revealed that the Galactic model choice significantly affects the results, finding H 0 = 69.0 4 − 2.07 + 2.30 km s − 1 Mpc − 1 with NE2001 model versus H 0 = 75.6 1 − 2.07 + 2.23 km s − 1 Mpc − 1 with YMW16 model. A Bayesian analysis of a sample of 16 localized FRBs and 60 unlocalized events observed with ASKAP and Parkes yielded H 0 = 7 3 − 8 + 12 k m s − 1 M p c − 1 (James et al., 2022b). Using probability distributions of D M host and D M IGM derived from the IllustrisTNG simulation, a suite of cosmological magnetohydrodynamical simulations of galaxy formation that provides physically motivated host-galaxy and intergalactic-medium DM distributions, an MCMC analysis of 108 localized FRBs constrained H 0 to 69.4 0 − 1.97 + 2.14 k m s − 1 M p c − 1 (Gao et al., 2025), while a Bayesian MCMC analysis of 64 localized FRBs, accounting for uncertainties in D M IGM, D M host, and D M Halo, yielded H 0 values ranging from 76.1 6 − 2.89 + 2.48 to 85.0 8 − 2.66 + 2.71 km s − 1 Mpc − 1 (Kalita et al., 2025). Finally, a comprehensive summary of current measurements is available in (Valentino et al., 2025).

The availability of a larger sample of localized FRBs provides an opportunity to re-examine the inference of H 0 and its dependence on the assumptions adopted for the different dispersion-measure components. In this work, we use a Bayesian MCMC framework like the one developed in previous studies (Wu et al., 2022; James et al., 2022b; Gao et al., 2025; Kalita et al., 2025; Xu et al., 2025; Wang et al., 2025), but we expand the analyses in several directions. First, we update the FRB sample to 126 localized FRBs; after applying conservative quality cuts, we retain 118 events. Second, we explore different prescriptions for host-galaxy dispersion measure contribution, including redshift-independent and redshift-dependent models for each subpopulation used in IllustrisTNG (Zhang et al., 2021) and calculate H 0 for each subpopulation. Third, we use a simulated sample constructed to reproduce the empirical distribution through a Weibull model.

The remainder of this paper is organized as follows. Section 2 details the theoretical framework for dispersion measure contributions from various media. Section 3 describes our FRB sample selection criteria and data processing. Section 4 outlines the Bayesian model used to determine H 0. Our results are presented in Section 5. Section 6 explores future prospects using simulated data. Finally, Section 7 summarizes our conclusions and discusses implications for FRB cosmology.

2 Dispersion measure components

The observed dispersion measure of Fast Radio Bursts results from the integrated column density of free electrons along the line of sight. When an FRB signal propagates through an ionized medium, there is a delay time between the highest ( ν 2 ) and lowest frequencies ( ν 1 ). The time delay Δ t between two frequencies ν 1 and ν 2 is given by Equation 1 (Lorimer et al., 2007; Deng and Zhang, 2014; Petroff et al., 2019):

Δ t = e 2 2 π m e c 1 ν 1 2 − 1 ν 2 2 ∫ n e , z 1 + z d l ≡ e 2 2 π m e c 1 ν 1 2 − 1 ν 2 2 D M o b s , (1)

where n e , z represents the electron number density at redshift z; e and m e are the electron charge and mass, respectively; c is the speed of light and the integral is taken along the line of sight from source to observer. The quantity D M o b s ≡ ∫ n e , z / ( 1 + z ) d l encapsulates the total column density of free electrons, with the ( 1 + z ) factor arising from the cosmic expansion affecting both the number density and the path length element.

The total observed dispersion measure can be decomposed into several components, as shown in Equation 2 (Gao et al., 2014; Deng and Zhang, 2014; Macquart et al., 2020):where, D M M W , I S M and D M M W , h a l o represent contributions from the Milky Way’s interstellar medium and extended halo, respectively; D M I G M ( z ) represents the effective cosmological line-of-sight contribution, including the diffuse intergalactic medium and the halos of galaxy clusters, groups, and galaxies (Connor et al., 2024), and D M h o s t accounts for the host galaxy and local environment near the FRB source.

D M o b s = D M M W , I S M + D M M W , h a l o + D M I G M z + D M h o s t 1 + z , (2)

Following Equation 2, the extragalactic term (D M e x t) can be isolated in two ways as shown in Equation 3:

D M e x t ≡ D M o b s − D M M W , I S M − D M M W , h a l o = D M I G M + D M h o s t 1 + z . (3)

This D M e x t contains the cosmological signal but remains contaminated by the poorly constrained host galaxy contribution.

The Milky Way’s ISM contribution D M M W , I S M can be estimated using electron density models such as NE2001 (Cordes and Lazio, 2002) or YMW16 (Yao et al., 2017). While these models generally agree at high Galactic latitudes, significant discrepancies emerge at lower latitudes (Ocker et al., 2021), with YMW16 model sometimes overestimating contributions in specific sightlines.

Galactic halo term D M M W , h a l o was estimated by Prochaska and Zheng (Prochaska and Zheng, 2019), who suggested values in the range 50 − 80pc cm − 3, while Macquart et al. (Macquart et al., 2020) adopted a conservative fixed value of 50pc cm − 3 in their analysis. However, recent investigations have suggested lower values, such as D M M W , h a l o = 43pc cm − 3 reported in (Yamasaki et al., 2020) using X-ray observations, while in (Kirsten et al., 2022) the value is constrained to D M M W , h a l o < 32 − 42pc cm − 3 using FRB 20200110E in M81. In this work, we adopt D M M W , h a l o = 65pc cm − 3 and estimate the deviations from H 0 for the other values.

On the other hand, the mean value of D M I G M ( z ) follows (Hagstotz et al., 2022; Zhou et al., 2014; Connor et al., 2024):where Ω b is the baryon density parameter, H 0 is the Hubble constant, f IGM is the fraction of baryons in the IGM, m p is the proton mass, and E ( z ) ≡ H ( z ) / H 0 is the dimensionless Hubble parameter. Hereafter, we adopt f IGM = 0.85 ± 0.05, following (Cordes et al., 2022). The electron ionization fraction χ e takes into account the ionization states of hydrogen and helium through χ e = Y H X e , H + 1 2 Y H e X e , H e, where X e , H and X e , H e are the ionization fractions of the intergalactic hydrogen and helium (Zhou et al., 2014), respectively and Y H ≈ 0.75 and Y H e ≈ 0.25 (Kurichin et al., 2021; Aver et al., 2015; Planck et al., 2020). For z < 3, both hydrogen and helium are generally considered fully ionized (Meiksin, 2009; Becker et al., 2011), so χ e ≈ 7 / 8.

⟨ D M I G M z ⟩ = 3 c H 0 Ω b f IGM χ e 8 π G m p ∫ 0 z 1 + z ′ E z ′ d z ′ , (4)

The actual distribution of DM IGM shows strong dispersion around this mean along different lines of sight due to inhomogeneities in the diffuse intergalactic medium and to variations associated with the halos of galaxy clusters, groups, and galaxies (Connor et al., 2024). The probability distribution that adequately describes these variations is given by (Macquart et al., 2020; Meiksin, 2009; Becker et al., 2011; McQuinn, 2013):where Δ ≡ D M I G M / ⟨ D M I G M ⟩ is the normalized IGM dispersion measure, σ IGM is the effective standard deviation, and the parameters α and β, which relate to the density profile of the internal gas within the halos, are set to a value of three following the approach of Macquart et al. (Macquart et al., 2020). Finally, A is a normalization constant and C 0 is a value chosen to ensure that the distribution has a mean of one. We use the values reported in Table 1 of (Zhang et al., 2021) estimated from the IllustrisTNG Simulation.

p IGM Δ = A Δ − β ⁡ exp − Δ − α − C 0 2 2 α 2 σ IGM 2 , Δ > 0 , (5)

TABLE 1. Localized FRB sample used in this work. The Type classification follows Zhang et al. (2020): Type 1 represents repeating FRBs similar to FRB 20121102A, Type 2 denotes repeaters like FRB 20180916B, and Type 3 corresponds to non-repeating FRBs. The Milky Way contributions were calculated using both the NE2001 (Cordes and Lazio, 2002) and YMW16 (Yao et al., 2017) models using a Python package fruitbat (Batten, 2019).

Unlike the well-understood contribution of the Milky Way, the host galaxy’s contribution to the measured dispersion remains largely unknown. Previous studies indicate that it depends on factors such as the host galaxy type, the burst environment, and the galaxy’s orientation, among others (Xu et al., 2025; Zhang et al., 2020). These dependencies lead to large variations. We adopt Prochaska’s proposal, a lognormal distribution (Niu et al., 2022; Macquart et al., 2020):which naturally accommodates the observed asymmetric tail toward high values. In studies based on IllustrisTNG simulations, Zhang classified FRBs into three types. Type 1: Repeaters like FRB 20121102, located in dwarf galaxies with a stellar mass about ( 4 − 7 ) × 1 0 7 M ⊙ and SFR of about 0.4 M ⊙ yr − 1. Type 2: Repeaters like FRB 20180916, located in a spiral galaxy. In this case, the stellar mass about 1 0 11 M ⊙ and S F R ≈ 0.016 M ⊙ yr − 1. Type 3: apparently non-repeating FRBs, which have similar host galaxies, with a stellar mass ranging in 1 0 9 − 1 0 11 M ⊙ and a star formation rate in the range 0.4 M ⊙ yr − 1.

p D M h o s t = 1 D M h o s t σ host 2 π exp − ln D M h o s t − μ host 2 2 σ host 2 , (6)

3 Data sample and selection criteria

We have compiled a database of 126 FRBs, as shown in Table 1.

From this database, we excluded the following FRBs for the reasons explained below: FRB 20190520B and FRB 20220831A are excluded due to their exceptionally high DM magnitudes; FRB 20210405I, FRB 20220319D and FRB 20230718A are excluded because their magnitudes are primarily dominated by the galactic contribution, making the extragalactic component uncertain, and this is the component we are interested in; FRB 20221027A is excluded due to a double association with host galaxies; FRB 20190110C and FRB 20191106C are excluded because they are repeaters but do not fit the classification given in (Zhang et al., 2020).

After applying these selection criteria, we were left with a database of 118 FRBs. This represents one of the largest compilations of localized FRBs used for Hubble constant measurements to date.

4 Bayesian methodological framework

Starting from the observed DM obs − z data, we apply a Bayesian approach. The posterior probability distribution for H 0 is written as Equation 7:where D M obs , i denotes the set of observed measured dispersions, L is the likelihood and π ( H 0 ) is the prior distribution of H 0.

p H 0 | D M obs , i ∝ L D M obs , i | H 0 ⋅ π H 0 (7)

On the other hand, if we have two random variables X ( x ) and Y ( y ) with probability distributions P X ( x ) and P Y ( y ), respectively, and we also have a new variable Z such that Z = X + Y, then the distribution of Z is obtained through the convolution given in Equation 8:

P Z z = ∫ 0 z P X x P Y z − x d x . (8)

In our case, we define the extragalactic D M ext as:

D M ext = D M IGM + D M host 1 + z , (9)

Therefore, the probability distribution for each D M ext, is given by Equation 10:

P i D M ext , i ∣ z , H 0 = ∫ 0 DM ext , i 1 + z P host D M host 1 + z i × P IGM D M ext , i − D M host 1 + z i | z , H 0 d D M host . (10)

The individual probabilities are combined over the full FRB catalog through the likelihood function in Equation 11:

L D M obs , i | H 0 = ∏ i = 1 N P D M ext , i | z i , H 0 , (11)

To obtain the posterior distribution, we used the emcee package (Foreman-Mackey et al., 2013) and employed a uniform prior distribution between 20 km s − 1 Mpc − 1 and 120 km s − 1 Mpc − 1.

5 Results

In this Section, we present seven host-galaxy models and the corresponding H 0 results. These models can be classified into.

• Redshift-independent lognormal host models (I, II, and III), in which a single pair of parameters ( μ host , σ host ) is assumed for the entire 118-FRB sample.
• Redshift-dependent host models (IV, V, VI, and VII). Models IV, V, and VI are class-specific prescriptions based on the IllustrisTNG classification in (Zhang et al., 2020), and are applied separately to the three FRB subpopulations (10, 8, and 100 FRBs, respectively). In contrast, Model VII is applied to the entire catalog by assigning to each FRB the host model corresponding to its class. For this reason, we expect Model VII to yield the most reliable result.

Table 2 shows the values used for each model, the number of FRBs used in each case, the H 0 values for the NE2001 and YMW16 models along with the difference between them. Finally, the results for independent z models are analyzed first, then the dependent z models, and finally the systematic differences between the NE2001 and YMW16 models.

TABLE 2. The seven different host galaxy models considered for determining H 0 are shown.

For each model, the following are shown: the number of FRBs used ( N FRB ), the mean of the host model exp ( μ ), the σ host used for dispersion, the value of H 0 for the two D M M W models used (NE2001 and YMW16), and the difference between these two predictions Δ H 0 = H 0 , Y M W 16 − H 0 , N E 2001, and the reference for each model. Models IV-VI correspond to the three FRB subpopulations defined in Zhang et al. (2020), while Model VII applies the corresponding host prescription to each individual FRB.

We assessed the impact of the assumed fraction of baryons in the intergalactic medium, f IGM = 0.85 ± 0.05 (Cordes et al., 2022). Repeating the analysis with f IGM = 0.80 and 0.90 yields variations in H 0 of approximately ± 5 % to ± 7 % across all models. These systematic shifts are comparable in magnitude to the statistical uncertainties reported in Table 2, suggesting that the f IGM uncertainty contributes at a level similar to the statistical error. In a similar manner, given the uncertainty in the Milky Way halo dispersion measure ( DM MW, halo ), with plausible values ranging from 50 to 80 pc cm − 3 (52, 53, 54), we assessed the impact of this uncertainty on our H 0 inference through a sensitivity study. This involved generating 20 realizations in which DM MW, halo for each FRB was drawn from a uniform distribution over the interval [50,80] pc cm − 3 to account for differences in the lines of sight. The mean of the resulting 20 posterior distributions deviates from the results reported in Table 2 by at most 0.58% (Model V). Furthermore, the dispersion of these 20 curves falls within the statistical uncertainties previously reported in Table 2. These tests demonstrate that the uncertainty in the halo dispersion measure does not dominate the error budget and that the results presented in this work are robust to plausible variations in this parameter.

As will be discussed later in this Section, models IV, V, and VI, which are applied to subpopulations, are not statistically very reliable, so in Figure 1, only the results where the calculation is performed for the entire catalog are shown (models I, II, III, and VII).

5.1 Host models independent of z

Models I, II, and III consider z-independent log-normal models for D M host, characterized by the σ and μ values shown in Table 2. The results show an expected degeneracy. Choosing a specific distribution for D M host affects the possible values of D M IGM and, therefore, H 0. Larger D M host values must be offset by smaller H 0 values to fit the observed D M obs.

Models I and II produce H 0 values similar to those of Model VII, which considers the characteristics of each FRB. Furthermore, these H 0 values are also intermediate between measurements of the early and late universe. Therefore, the σ and μ settings within these parameters adequately capture, on average, the characteristics of this FRB population. Given the consistency between the NE2001 and YMW16 models, Model I would be a better choice as a z-independent reference model. If Model III is included in the analysis, it is observed that as the values of the host distribution parameters increase, the H 0 value decreases to compensate and make the complete model compatible with the observed data. For Model III, an extremely low H 0 value is obtained. This suggests a degeneracy between these parameters, so we can improve the host description by using a z-dependent model that selects the appropriate host model for each FRB, as proposed in (Zhang et al., 2020).

5.2 Host models dependent on z

In (Zhang et al., 2020), FRBs were classified into three groups (types I, II, and III), and using IllustrisTNG simulations, the parameter values of the D M host distribution were calculated for each type. Our catalog contains FRBs of these three types, and therefore, using the values reported in (Zhang et al., 2020), we calculated the H 0 value for each subpopulation.

Model IV corresponds to repeaters like FRB 20121102 (type I) located in dwarf galaxies. The number of FRBs of this type in our catalog is 10, so while the predicted H 0 value is quite good, H 0 = 71.6 0 − 7.32 + 6.50 km s − 1 Mpc − 1 for NE2001 model, it should be interpreted with caution due to the small sample size. The results for YMW16 model are not as encouraging; we obtain H 0 = 84.8 4 − 8.09 + 7.26 km s − 1 Mpc − 1, which is the largest discrepancy NE2001-YMW16 in all our work, and exhibits extreme divergences between the D M MW values for the lines of sight, which are included here.

Type 2 FRBs, which are repeaters like FRB 20180916 and are located in spiral galaxies, are considered in Model V. Our catalog contains 8 of these FRBs, and applying the Bayesian scheme leads to extraordinarily low H 0 values: H 0 = 36.2 2 − 7.76 + 9.73 km s − 1 Mpc − 1 for NE2001 model and 37.5 2 − 6.07 + 5.96 km s − 1 Mpc − 1 for YMW16 model. This consistency between the two models for D M MW suggests that the fit obtained from the IllustrisTNG simulations might overestimate the contribution of D M host and that some adjustment is required.

Model VI for non-repeating FRBs, or those that have not yet been repeated, has a much larger population than the two previous models in our catalog (100 FRBs). However, it generates unexpectedly high H 0 values: H 0 = 79.2 7 − 2.30 + 2.67 km s − 1 Mpc − 1 for NE2001 model and H 0 = 80.3 9 − 2.40 + 2.26 km s − 1 Mpc − 1 for YMW16 model. The difference between the two models for D M MW is the smallest of all the results (Δ H 0 = + 1.12 km s − 1 Mpc − 1), indicating high consistency in this line of reasoning, but also suggesting that fitting this population might be underestimating the host contribution and forcing very high values for the IGM dispersion measure and, consequently, for the H 0 value.

Applying this Bayesian methodology to each type of FRB described in this Section yields somewhat unexpected results. Model V produces an extremely low value (H 0 ∼ 36 km s − 1 Mpc − 1), while model VI generates an excessively high value (H 0 ∼ 85 km s − 1 Mpc − 1). While the small population sizes of models IV and V make their results statistically unreliable, such a high value would not be expected for model VI (non-repeaters), given that its population is similar to the total population. On the other hand, the large value of Δ H 0 ∼ + 13 km s − 1 Mpc − 1 for model IV indicates a strong influence of the D M MW model (NE2001 vs. YMW16) in this population, making the H 0 = 71.6 0 − 7.32 + 6.50 km s − 1 Mpc − 1 value obtained for NE2001 model unreliable.

The findings obtained from models IV, V, and VI, which follow the classification proposed in (Zhang et al., 2020), suggest that this classification may need to be revised. However, the number of FRBs in these subpopulations is still too low to make definitive statements. Furthermore, the IllustrisTNG simulations have several limitations that could affect these findings. The main limitations are as follows. First, with a baryonic mass resolution of 1.4 × 1 0 6 M ⊙ and typical cell sizes of order kiloparsec, TNG100 does not resolve the parsec-scale environment around the FRB source (Pillepich et al., 2017). A dense, localized plasma can contribute a substantial and highly uncertain DM that may exceed the contribution from the galactic disk or halo (Zhang et al., 2020). Second, the simulation uses subgrid prescriptions for the multiphase ISM and imposes a temperature floor of ∼ 1 0 4 K (Springel and Hernquist, 2003); cold gas phases are not explicitly resolved. Third, the model parameters were calibrated to reproduce a selected set of observables that did not include FRB host DMs. Different feedback implementations would yield different galaxy gas distributions (Pillepich et al., 2017). Fourth, the simulation does not define a unique boundary for subhalos, introducing uncertainty in the integration path length. Fifth, the host DM distributions in Zhang et al. (2020) are derived from only eight discrete redshifts, with interpolation between them, which may lead to inaccurate estimates of the variance in DM evolution.

Despite the previous results, if we consider the total population of FRBs (118 FRBs = 10 type I + 8 Type II + 100 Type III) and assign the corresponding host-galaxy model to each FRBs, we obtain a value H 0 = 71.3 6 − 3.94 + 3.59 km s − 1 Mpc − 1 (NE2001 model), as shown in Table 2 and Figure 1, under the name of model VII. This result is the main one of this work, as it considers the largest amount of data while preserving each data set’s particularities, and it provides an intermediate value between Planck and SH0ES measurements, which would alleviate the Hubble Tension. However, with the YMW16 model, the value obtained is H 0 = 75.2 6 − 2.06 + 2.05 km s − 1 Mpc − 1, and the estimate shifts towards higher values. On the other hand, as shown in Figure 2, the error bars overlap the Planck and SH0ES values. This does not yet allow us to make definitive statements about our findings. However, the behavior of our methodology in a scenario with a larger number of data points is explored in Section 6 using simulated data, which provides an internal forecast under the adopted assumptions.

Finally, while our main result is promising, the subpopulation predictions are intriguing. In summary, they suggest that the FRB classification captures their nature, that combining all types mitigates the intrinsic biases of each, but that the models for each type can be improved.

5.3 Systematic differences between NE2001 and YMW16 models

The differences between the predictions of the NE2001 and YMW16 models are calculated in each case as Δ H 0 = H 0 , Y M W 16 − H 0 , N E 2001, and are shown in Table 2. Across all our results, differences in the predictions of the two galactic models are observed. While the direction of the difference is systematic (always H 0 , Y M W 16 > H 0 , N E 2001), the magnitude of these differences is highly variable (from + 1.12 km s − 1 Mpc ⁻¹ to + 13.24 km s − 1 Mpc ⁻¹).

For models I-III, which are independent of z, we obtain differences between + 1.52 km s − 1 Mpc ⁻¹ and + 4.72 km s − 1 Mpc ⁻¹, while for the FRB subpopulations, the differences range from + 1.12 km s − 1 Mpc ⁻¹ to + 13.24 km s − 1 Mpc ⁻¹, with model IV showing the largest difference. For our main result in model VII with class awareness, the difference is + 3.90 km s − 1 Mpc ⁻¹. These systematic differences and their errors are shown for models I, II, III, and VII in Figure 2, along with the reference values (Riess et al., 2022) and (Planck et al., 2020).

It is noteworthy that the error of our main result (3.94 km s − 1 Mpc − 1) is similar to the difference between the predictions of models (3.90 km s − 1 Mpc − 1), so at this time it is not possible to favor either of the two models.

6 Future prospects

6.1 Distributional fit of the redshift sample

A set of parametric families was considered to model the empirical redshift distribution: Normal, Exponential, Lognormal, and Weibull. Each family was fitted by maximum likelihood using scipy.stats. Goodness-of-fit was assessed with the Kolmogorov–Smirnov (KS) statistic, and parsimony was compared with the Akaike (AIC) and Bayesian (BIC) information criteria. Higher log-likelihood (LL) indicates better fit, whereas lower KS, AIC and BIC indicate better fit. The results of these metrics for the distributions mentioned are shown in Table 3.

TABLE 3. Goodness-of-fit summary for the four parametric models of the redshift distribution.

For each candidate distribution, the Table lists the Kolmogorov–Smirnov (KS) statistic, the maximized log-likelihood (LL), and the corresponding Akaike (AIC) and Bayesian (BIC) information criteria. Higher LL and lower KS, AIC and BIC indicate better agreement with the data.

Across metrics, the Weibull distribution attains the lowest KS and the lowest AIC (the latter only slightly, Δ A I C ≈ 0.12 versus Exponential), as well as the highest log-likelihood; meanwhile, BIC marginally favors the Exponential (Δ B I C ≈ 2.65 in its favor). Using a simple majority decision among KS, AIC, and BIC, the selected model is the Weibull distribution.

This distribution is a flexible family for modeling positive-valued data. Under the selected model, the probability density function for z ≥ 0 is given by Equation 12:

f z ∣ k , λ = k λ z λ k − 1 ⁡ exp − z λ k . (12)

The shape parameter k determines the basic form of the distribution: k < 1: decreasing failure rate (high probability at low z with long tail), k = 1: reduces to the exponential distribution and k > 1: unimodal with increasing failure rate (peak at intermediate z). On the other hand, the scale parameter λ characterizes the typical redshift scale, with 63.2% of the probability below z = λ.

The maximum-likelihood estimates for our data are k = 1.13 and λ = 0.27. For reference, when k > 1, the mode is z mode = λ ( k − 1 ) / k 1 / k and the mean is E [ z ] = λ Γ 1 + 1 / k, which, at our estimates, gives z mode ≈ 0.041 and E [ z ] ≈ 0.261. The observed z distribution is shown in Figure 3 along with the Weibull distribution fit.

6.2 Mock FRB sample generation conditioned on the empirical redshift

The simulated catalog is built within the same physical and statistical framework presented in the previous sections, so it involves an unavoidable methodological circularity and should be interpreted as an internal forecast of the statistical performance of the method and not as an external validation.

To generate simulated FRBs consistent with the observed redshift sample, we use the same parameter values and apply the following pipeline.

• For each seed s ∈ { 1 , … , 20 }, 700 redshifts ( z i ) were generated with a distribution that follows the Weibull distribution fitted in the previous subsection.
• For every z ∈ z i, ⟨ D M IGM ( z ) ⟩ was computed by Equation 4.
• Scatter about ⟨ D M IGM ( z ) ⟩ was modeled through a redshift-dependent distribution in Equation 5, so D M IGM ( z ) = Δ IGM ( z ) ⟨ D M IGM ( z ) ⟩.
• For each seed, the host terms are drawn from a lognormal distribution (Equation 6), with parameters e μ host ∼ U ( 50,80 pccm − 3 ) and σ host ∼ U ( 0.3 , 0.8 ).
• The extragalactic total dispersion measure DM ext , i is obtained from Equation 9. A selection criterion is then applied, retaining only realizations with 100 pccm − 3 < D M ext , i < 1400 pccm − 3. After this cut, a simple random subsample of 500 events (without replacement) is kept for that seed.
• Finally, we obtain a sample of simulated FRBs (z i, DM ext , i)

Figure 4 shows one of these 20 realizations. We use the simulated data and repeat the same routine mentioned in Section 4. Since Model I similarly captures the behavior of the more flexible Model VII, we chose Model I on grounds of simplicity and numerical stability. Only one is used for the calculations; the other 19 realizations with the remaining seeds were used to check for consistency, revealing that the maximum difference between the H 0 results was 1.2%.

The result is H 0 = 69.5 1 − 0.84 + 0.86 km s − 1 Mpc − 1, which exhibits high symmetry, as shown in Figure 5. This value differs by 2.6% from that obtained with Model VII using the observed data. Given how the catalog was constructed, this level of agreement should be interpreted only as internal consistency under the adopted assumptions rather than as an independent validation of the methodology. More important than the value itself is that the statistical precision decreases from 5.5% with 118 FRBs (observed) to 1.2% with 500 FRBs (simulated). This indicates that, in the near future, with the confirmation of a few hundred more FRBs, we will achieve statistical precision comparable to that of Planck and Riess.

To evaluate the impact of errors in the parameters f IGM, Ω b, Ω m, and χ e on the H 0 results, we varied their values from their central values, taking into account the reported errors, and repeated the procedure. We found that the inferred value of H 0 varied by up to 0.3 % for f IGM, 0.3 % for Ω b, 0.4 % for Ω m, and 1.3 % for χ e. These tests show that the sensitivity to changes in these parameters is low and that these variations are contained within the error of H 0.

7 Conclusion

Using a catalog of 126 FRBs, we applied a Bayesian approach to determine the value of the Hubble constant, seeking to alleviate the Hubble tension, one of the major challenges of modern cosmology. After applying several selection criteria, we were left with 118 FRBs, distributed across three subpopulations: 100 non-repeating FRBs to date, 10 repeating FRB 20121102, and 8 repeating FRB 20180916.

For this population, we proposed studying seven different models for the Host Galaxy Dispersion Measure ( D M host ) and two models for the Milky Way Dispersion Measure (NE2001 and YMW16). In the first three (models I-III), we proposed z-independent models for D M host in all FRBs and obtained values ranging from H 0 = 57.5 8 − 2.09 + 2.10 km s − 1 Mpc − 1 to H 0 = 76.3 5 − 1.81 + 1.83 km s − 1 Mpc − 1. It was observed that parameters like e μ = 66 pccm⁻³ and σ host = 0.42 accurately capture, on average, the characteristics of the studied FRB population. A degeneracy was found between the D M host parameters and H 0. The values of H 0 are strongly conditioned by the choice of μ and σ host.

Models IV, V and VI correspond to the models found in (Zhang et al., 2020) through IllustrisTNG simulations for each of the three subpopulations. The results range from H 0 = 36.2 2 − 7.76 + 9.73 km s − 1 Mpc − 1 to H 0 = 84.8 4 − 8.09 + 7.26 km s − 1 Mpc − 1. Besides demonstrating high dispersion (∼36–85 km s − 1 Mpc − 1), they are unreliable for several additional reasons: the number of data points for models IV and V is very low, 10 and 8, respectively; model IV, which generates a plausible value with NE2001 model (H 0 = 71.6 0 − 7.32 + 6.50 km s − 1 Mpc − 1), shows an unusually high difference relative to the value obtained using YMW16 model (H 0 = 84.8 4 − 8.09 + 7.26 km s − 1 Mpc − 1); and model VI (100 FRBs), which has the highest subpopulation, shows excessively high values. The large deviations from the expected range above motivate us to seek better fits for each repeater type in future work.

The main model used in this work was Model VII. In this model, we respected the host type for each FRB and calculated using the complete catalog. This yields the main result of this work:

H 0 , NE 2001 = 71.3 6 − 3.94 + 3.59 km s − 1 Mpc − 1 (13)

This value is the most reliable, both due to the amount of data and because it respects the environmental characteristics of each FRB. This intermediate value suggests that FRBs may act as potential arbiters in the ongoing Hubble Tension. However, two aspects should be highlighted. First, the value for the YMW16 model in this case is H 0 = 75.2 6 − 2.06 + 2.05 km s − 1 Mpc − 1 and the difference with the value in Equation 13 is not as small as in other cases (+ 3.90km s − 1 Mpc − 1) and is similar to the errors obtained (+ 3.94km s − 1 Mpc − 1), which makes it difficult to decide on a model for D M MW. Second, the errors themselves are not small and have a statistical precision of 5.5%, which is not comparable to those of (Planck et al., 2020; Riess et al., 2022), of 0.7% and 1.4%. While a systematic analysis of the differences between the models for D M MW is beyond the scope of this work, we explore the second aspect through a mock FRB catalog.

We generated a catalog of simulated FRBs, using a Weibull distribution for the redshifts ( z i ) and calculated DM ext , i using the same methodology used for the observed values. The value obtained is H 0 = 69.5 1 − 0.84 + 0.86 km s − 1 Mpc − 1. This value differs by 2.6% from our main result. However, since the mock catalog was generated within the same general framework, this agreement should not be interpreted as an external validation of the methodology, but rather as an internal assessment of its statistical behavior under the adopted assumptions. More importantly, the result represents an improvement in statistical accuracy from 5.5% with 118 FRBs to 1.2% with 500 FRBs, suggesting that, in the near future, with a few hundred additional FRBs, this method will achieve a precision comparable to that of current reference methods.

Our findings show that FRBs can be used as probes of cosmological parameters, such as the Hubble constant, and that, in the near future, they may achieve a level of statistical accuracy comparable to that of traditional probes. Our study also reveals several issues that must be addressed to improve the results: systematic differences between models for DM MW and their impact on cosmological parameters, and the need to refine the DM host model.

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Footnotes

Edited by: Jirong Mao, Chinese Academy of Sciences (CAS), China

Reviewed by: Ece Kilerci, Istanbul University, Türkiye

Qin Wu, Nanjing University, China