Fast radio bursts as cosmological proxies: estimating the hubble constant

One of the most challenging problems in modern cosmology is the Hubble tension, a discrepancy in the predicted expansion rate of the Universe with different observational techniques that results in two conflicting values of $H_0$. We leverage the sensitivity of the Dispersion Measure (DM) from Fast Radio Bursts (FRBs) with the Hubble factor to investigate the Hubble tension. We build a catalog of 98 localized FRBs and an independent mock catalog and employ three methods to calculate the best value of the Hubble constant: i) the median value of $H_0$ derived from direct computation combined with bootstrap resampling, ii) the Maximum Likelihood Estimate (MLE), and iii) the reconstruction of the cosmic expansion history $H(z)$ using two DM-$z$ relations previously explored in the literature. The values found vary between 53 and 80 $\text{km/s/Mpc}$. The result with the best statistical precision (6.0%) is the one obtained through MLE: $H_0=70.10_{-3.63}^{+4.19}\text{\hspace{0.17em}km/s/Mpc}$. On the other hand, when using 100 mock catalogs of 500 simulated FRBs in each realization, we obtain a value for the Hubble constant changes to $H_0=67.30_{-0.85}^{+0.98}\text{\hspace{0.17em}km/s/Mpc}$. More importantly, the latter result notably increases the statistical precision to 1.5% (the same level of precision as reports from the SH0ES collaboration). Ultimately, the rapid increase in the number of confirmed FRBs will provide us with a robust prediction of the value of the Hubble parameter today, which, in combination with other cosmological observations, will allow us to alleviate (to a certain degree) the current Hubble tension and make inference of other cosmological observables.

1 Introduction

Fast Radio Bursts (FRBs) are bright millisecond transients detected in the radio waveband, ranging from 100 MHz to 8 GHz. Although their origin has not yet been discovered, nor the mechanisms that fuel these short bursts of energy, they have been depicted as having cosmological origin; therefore, they could be used to identify the properties of their galaxy hosts and the intergalactic medium through which their light goes before reaching our telescopes.

Besides the 2D angular coordinates, the main observable used to study FRBs is their dispersion measure (DM), which quantifies the properties of the medium where their light passes through, more specifically, the integrated number of free electrons along the path that interacts with their photons and causes a difference in the frequencies of light emitted by the object. This interaction between the FRB’s photons and free electrons causes a difference between the radiation’s highest and lowest frequencies, allowing us to infer the total DM.

Different authors have claimed that three components contribute to the total ${\text{DM}}_{\text{obs}}$ (Pol et al., 2019; Zhang et al., 2020a; Zhu and Feng, 2021), among them, the dispersion due to our galaxy, ${\text{DM}}_{\text{MW}}$, and due to their extragalactic origin, a term due to the intergalactic medium (IGM), ${\text{DM}}_{\text{IGM}}$, and a third one caused by the interaction of the FRB photons with their host galaxy, ${\text{DM}}_{\text{host}}$. The second and third terms have intricate dependencies on redshift $z$, explained mainly by their cosmological origins. Although the modeling of each one of the latter terms is complex and constitutes an extensive field of study of FRBs.

To date, a few thousand FRBs have been detected, and the census is rapidly growing with the new radio telescopes that come online that observe and characterize these transients. Only a tiny fraction of these reported FRBs in the literature has direct information about their $z$ because their galactic progenitors cannot be identified with radio observations; thus, other wavelength surveys need to observe the patch of the sky where the FRB is detected to have an inferred $z$ and complete their localization. However, less than a hundred FBRs have been detected with known $z$ (i.e., their hosting galaxy is identified), many of which are at low redshift.

Recent studies focus on modeling the relationship between the observed DM and their corresponding $z$. For instance, (Macquart et al., 2020; Cui et al., 2022; Baptista et al., 2023) presented different fits for a linear relation in DM vs. $z$. In particular, (Piratova-Moreno and García, 2024) presents a revision of different ${\text{DM}}_{\text{obs}}$ models as a function of the redshift based on physical motivations. In the latter work, the authors used 24 FRBs with $z$ known to propose different relations for ${\text{DM}}_{\text{obs}}$($z$): a linear trend, a log parabolic relation, a power-law model, and as a separate stage, an interpolation that not only takes into account $z$, but also the angular coordinates of each FRB, following results from (Xu et al., 2021).

On the other hand, FRBs could offer a new window for cosmological studies because of their random distribution in the sky. Eventually, it will allow us to cross-correlate their position with galaxy redshift surveys. Despite the increasing number of cosmological FRBs, those with $z\ge$ 0.5, there is an inner challenge in deriving cosmological parameters and delivering information about the state of the intergalactic medium through the study of the dispersion measure of these transients due to the small sample of identified FRBs. Nonetheless, astronomers can use a combined analysis with other cosmological observations, such as the luminosity distance of SNIa, inferred cosmology from the cosmic microwave background (CMB), Gamma Ray Bursts (GRB), Big Bang Nucleosynthesis (BBN), Baryon Acoustic Oscillations (BAO), among others, to derive solid constraints on the value of the fine-structure constant, the value of the baryon fraction ${\mathrm{\Omega }}_b$ (given the correlation with the number of free electrons calculated from the DM), the equation of state of the dark energy (Deng and Zhang, 2014a; Zheng et al., 2014), and $H_0$ (the Hubble constant measured today) (Valentino et al., 2025). Notably, FRB studies provide an independent method to calculate a value of $H_0$, which would benefit the astronomical community currently facing the so-called “Hubble tension” (Di Valentino et al., 2021; Kamionkowski and Riess, 2023; Verde et al., 2024). The Hubble tension invokes a large discrepancy between the values of $H_0$ inferred from the CMB: 67.4 $\pm$ 0.5 km/s/Mpc (Aver et al., 2015), and a recent release of SNIa: 73.0 $\pm$ 1.0 km/s/Mpc (Riess et al., 2022), measured in the local universe from the SH0ES collaboration. Since the dispersion measure of the FRBs accounts for the distance between the transient and us, the DM is related to $H_0$ through the Hubble parameter in a non-trivial way and, thus, can be used as a proxy to estimate $H_0$.

Different groups have started a campaign to derive values of $H_0$ based on the current FRBs available. For instance (Hagstotz et al., 2022), reported $H_0=62.3\pm 9.1$km/s/Mpc using 9 FRBs and Maximum Likelihood Estimation method. On the other hand (Wu et al., 2022), presented a final value $H_0=$ ${68.81}_{-4.33}^{+4.99}$ km/s/Mpc using 18 localized FRBs with a theoretical approach. With the same number of FRBs (Liu et al., 2023), reported a value of 71$\pm 3$km/s/Mpc. Using 16 FRBs observed with ASKAP (James et al., 2022), reported $H_0=73_{-8}^{+13}$ km/s/Mpc. Moreover (Zhao et al., 2022), reported $H_0=80.4_{-\mathrm{19,4}}^{+24.1}$ km/s/Mpc for the expansion rate today with 12 unlocalized FRBs and BBN constraints. Furthermore (Hoffmann et al., 2024), reported $H_0=64_{-13}^{+15}$km/s/Mpc, making use of 26 selected FRBs from the DSA, FAST and CRAFT surveys. On the other hand (Yang et al., 2025), reported $H_0=74_{-7.2}^{+7.5}$km/s/Mpc using 30 FRBs and the temporal scattering of the FRB pulses due to the propagation effect through the host galaxy plasma. Applying Monte Carlo simulation to 69 localized FRBs (Gao et al., 2024), presented a value of Hubble constant $H_0=70.41_{-2.34}^{+2.28}$km/s/Mpc. Finally (Wang et al., 2025), performed an analysis combining 92 localized FRBs with data for DESI Y1 (Medina et al., 2025), indicating a preference for a dynamical dark energy model ${\omega }_0$-${\omega }_a$ over the standard $\mathrm{\Lambda }$CDM cosmology. In this parametrization, $w_0$ and $w_a$ describe the present value and the redshift evolution of the dark energy equation of state, respectively. Using the FRB subset-only, and values $H_0=69.04_{-2.07}^{+2.30}$ km/s/Mpc and $H_0=75.61_{-2.07}^{+2.23}$ km/s/Mpc, assuming galactic electron density models NE 2001 (Cordes and Lazio, 2002) and YMW16 (Yao et al., 2017), respectively. The most updated summary of inferred values for $H_0$ can be found in (Zheng et al., 2014).

In a similar fashion, we extend the catalog of FRBs presented in (Piratova-Moreno and García, 2024) to the latest 98 localized FRBs in the literature to perform a thorough statistical analysis and find a robust value for $H_0$. We use the Maximum Likelihood Estimate (MLE) method and median to find the best value of $H_0$ with the FRBs in the observed catalog. Then we calculate the value of $H_0$ assuming two of the models explored in (Zheng et al., 2014): the linear trend and the power-law function of the ${\text{DM}}_{\text{obs}}$ with $z$ and follow the evolution of $H(z)$, as explored in (Zheng et al., 2014). Finally, we create a synthetic catalog of FRBs (increasing the observed sample by a factor of 5) to derive the best-fit value of $H_0$ with each one of the methods described with confirmed FRBs.

The outline of this work goes as follows: Section 2 describes in detail how the different contributions to the dispersion measure (DM) are modeled. Section 3 is devoted to presenting our statistical analysis to retrieve the best values of $H_0$ implementing three completely different methods and the confirmed FRBs. Section 4 shows the analysis made with mock catalogs and presents the values obtained for the Hubble constant in this way. Finally, Section 5 presents the main conclusions found in this work. Throughout the paper, we have assumed a flat $\mathrm{\Lambda }$CDM model with cosmological parameters from (Planck et al., 2020).

2 Dispersion measure (DM)

As Fast Radio Burst (FRB) signals travel toward Earth, they undergo dispersion, resulting in a time delay between the arrival of different frequencies. This delay is quantified using the dispersion measure (DM) as shown in Equation 1 (Fortunato et al., 2024; Rajwade and Leeuwen, 2024; Glowacki and Lee, 2025):

$\mathrm{\Delta }t\propto \left({\nu }_{\text{lo}}^{-2}-{\nu }_{\text{hi}}^{-2}\right)\cdot \text{DM},(1)$

with ${\nu }_{\text{lo}}$ and ${\nu }_{\text{hi}}$ are the lowest and highest frequencies of the emitted signal, respectively. The dispersion measure is associated with the column density of free electrons along the signal’s path and is expressed as (Macquart et al., 2020; Fortunato et al., 2024; Glowacki and Lee, 2025):

$\text{DM}=\int \frac{n_e}{\left(1+z\right)}dl,(2)$

where $n_e$ is electron density in the comoving frame, and $dl$ is the differential proper distance. The observed dispersion measure $(\mathrm{D}{\mathrm{M}}_{\mathrm{o}\mathrm{b}\mathrm{s}})$ is estimated as the sum of the main contributions from different propagation environments (Macquart et al., 2020; Gao et al., 2014; Deng and Zhang, 2014b):

${\text{DM}}_{\text{obs}}={\text{DM}}_{\text{IGM}}+{\text{DM}}_{\text{MW}}+\frac{{\text{DM}}_{\text{host}}}{1+z},(3)$

here, the dispersion measure due to the Milky Way is ${\text{DM}}_{\text{MW}}$, which is mainly produced by the warm ionized medium. This component can be estimated using Galactic electron density models such as NE 2001 (Cordes and Lazio, 2002) and YMW16 (Yao et al., 2017); ${\text{DM}}_{\text{IGM}}$ represents the dispersion generated by the electron column in intergalactic space along the line of sight and and contains the information of the cosmological parameters and ${\text{DM}}_{\text{host}}$ corresponds to the dispersion that occurs in the host galaxy and this is corrected by a factor of ${(1+z)}^{-1}$, since the host galaxy’s contribution is measured in the observer’s frame. We will discuss the different contributions one by one below. On the other hand, the data of localized FRBs (i.e., with confirmed $z$) to date are shown in Figure 1; Supplementary Table 2.

Figure 1

Figure 1. Dispersion measure (DM) vs. redshift $(z)$ for confirmed FRBs. The size of the points is larger than the reported errors, so they are not included in the figure; Supplementary Table 2 shows the errors for the data that have them reported. The complete information of these transients is presented in Supplementary Table 2.

2.1 Dispersion measure due to the Milky Way

The Milky Way's contribution to the dispersion measure, ${\text{DM}}_{\text{MW}}$, arises primarily from the warm ionized medium (WIM) of the Galactic interstellar medium (ISM). This component consists of diffuse ionized gas distributed throughout the Galactic disk, its spiral arms, and the halo. This galactic contribution is usually estimated using empirical models built upon the observed dispersion measures of pulsars. The strength of this approach lies in how pulsars serve as natural probes, providing extensive sampling of the Galactic electron density along many lines of sight. Among the various models, two have become standard in the field: NE 2001 (Cordes and Lazio, 2002) and YMW16 (Yao et al., 2017).

The NE2001 model describes the Galaxy contribution taking in a count distinct components such as: spiral arms, the Galactic center, and localized clumps and voids. On the other hand, YMW16 model refines the parameters of the Galaxys large-scale structure, however, several studies have reported that YMW16 tends to overestimate ${\text{DM}}_{\text{MW}}$ in some directions (Price et al., 2021). It is for this reason that we adopt NE2001 model for the Galactic contribution. It is worth noting, however, that for our particular FRB sample, the results from YMW16 differ by only $\sim 1.5\%$, a minor discrepancy.

The ${\text{DM}}_{\text{MW}}$ values derived from both models are summarized in Supplementary Table 3 (Supplementary Appendix 2). Regarding the model’s uncertainty, NE2001 has been shown to reproduce pulsar observations with an uncertainty of approximately ${\sigma }_{\text{MW}}\sim 30,\mathrm{p}\mathrm{c},\mathrm{c}{\mathrm{m}}^{-\mathrm{3}}$ (Manchester et al., 2005). We therefore adopt this value as the Gaussian uncertainty associated with the Milky Way’s contribution.

2.2 Dispersion measure due to the galaxy host (DM_host)

The contribution to $\text{DM}$ from the host galaxies can be well described using a log-normal distribution (Macquart et al., 2020), since this is positive definite and captures the asymmetric long tail accounts for the possible excess DM introduced by gas surrounding the FRB source, such as HII regions, supernova remnants, or the circumstellar medium. Formally, the host-galaxy dispersion measure $({\text{DM}}_{\text{host}})$ is modeled using the probability distribution shown in Equation 4:

$p_{\text{host}}\left({\mathrm{D}\mathrm{M}}_{\text{host}}\right)=\frac{1}{{\mathrm{D}\mathrm{M}}_{\text{host}}{\sigma }_{\text{host}}\sqrt{2\pi }}\exp \left(-\frac{{\left(\ln {\mathrm{D}\mathrm{M}}_{\text{host}}-\mu \right)}^2}{2{\sigma }_{\text{host}}^2}\right)(4)$

The $1/\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}}$ factor arises from the Jacobian term associated with transforming from a Gaussian distribution in $\ln (\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}})$ to the log-normal distribution in $\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}}$, ensuring proper normalization over $\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}}>0$. The parameters $\mu$ and ${\sigma }_{\text{host}}$ correspond, respectively, to the mean and standard deviation of $\ln (\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}})$, and thus ${\sigma }_{\text{host}}$ is dimensionless. In terms of $\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}}$, this distribution has a median value of $\exp (\mu )$ and a standard deviation given by $\exp (\mu )e^{{\sigma }_{\text{host}}^2/2}{(e^{{\sigma }_{\text{host}}^2}-1)}^{1/2}$.

The findings reported by (Zhang et al., 2020b), based on the IllustrisTNG simulation, are consistent with this model. In that work, the authors estimated $\mathrm{D}{\mathrm{M}}_{\mathrm{h}\mathrm{o}\mathrm{s}\mathrm{t}}$ for non-repeating FRBs and two different types of repeaters: repeaters like FRB121102 and repeaters like FRB180916. For simplicity, we assume a uniform model for all FRBs, given by the best-fit parameters for the host galaxy dispersion measure distribution of one-off FRBs are given by $e^{\mu }=32.97{(1+z)}^{0.84}$ pc ${\text{cm}}^{-3}$ or the median and ${\sigma }_{\text{host}}=1.27$.

2.3 Intergalactic medium dispersion measure (DM_IGM)

From Equation 2, we use the redshift differential $dz$ to express the proper distance differential $dl$, as shown in Equation 5

$dl=\frac{c}{H_0\left(1+z\right)E\left(z\right)}dz.(5)$

since $E(z)=H(z)/H_0$, ${\text{DM}}_{\text{IGM}}$ average can be expressed as shown in Equation 6:

$⟨{\text{DM}}_{\text{IGM}}\left(z\right)⟩=\frac{c}{H_0}{\int }_0^z\frac{n_e\left(z^{\prime }\right)f_{\mathit{IGM}}\left(z^{\prime }\right)}{{\left(1+z^{\prime }\right)}^{2}E\left(z^{\prime }\right)}d{z}^{\prime },(6)$

where, we include $f_{\text{IGM}}(z)$ –the fraction of cosmic baryons in the ionized intergalactic medium–to exclude baryons locked in stars, compact objects, and dense interstellar medium (ISM). Hereafter, we adopt $f_{\text{IGM}}=0.85\pm 0.05$, following (Cordes et al., 2022). For the redshift range considered, where almost all baryons are ionized, the cosmic electron density can be approximated as a function of the baryon abundances (Hagstotz et al., 2022):

$n_e\left(z\right)\approx {\chi }_e\frac{\overline{{\rho }_b}\left(z\right)}{m_p}(7)$

where $\overline{{\rho }_b}$ is the mean baryon density, $m_p$ the proton mass, and the electron fraction ${\chi }_e=Y_H+\frac{1}{2}{Y}_{He}$. Assuming that the primordial abundances of Hydrogen and Helium satisfy the relationships $Y_H\approx 1-Y_{He}$ and $Y_{He}=0.2436\pm 0.0040$ (Kurichin et al., 2021), as determined by CMB measurements (Planck et al., 2020) and spectroscopic observations (Aver et al., 2015), ${\chi }_e\approx 1-\frac{1}{2}{Y}_{He}$, we assume ${\chi }_e\approx 0.8782\pm 0.0020$ according to (Kurichin et al., 2021). On the other hand, mean baryonic mass density ${\bar{\rho }}_b(z)$ evolves, as shown in Equation 8

${\bar{\rho }}_b\left(z\right)={\mathrm{\Omega }}_b{\rho }_c\left(0\right){\left(1+z\right)}^3,(8)$

where ${\mathrm{\Omega }}_b$ is the dimensionless baryon density parameter and ${\rho }_c(0)=\frac{3H_0^2}{8\pi G}$ is the current critical density, we thus obtain:

$n_e\left(z\right)=\frac{3H_0^2}{8\pi G}\frac{{\chi }_e{\mathrm{\Omega }}_b}{m_p}{\left(1+z\right)}^3.(9)$

Finally, we obtain the average contribution of the IGM can be written as follows:

$⟨{\text{DM}}_{\text{IGM}}\left(z\right)⟩=\frac{3c{\mathrm{\Omega }}_b{H}_0}{8\pi G{m}_p}{\chi }_e{f}_{\text{IGM}}{\int }_0^z\frac{1+z^{\prime }}{E\left(z^{\prime }\right)}d{z}^{\prime }.(10)$

However, because the intergalactic medium is not homogeneous, strong fluctuations around this value may occur. To capture these fluctuations, ${\mathrm{D}\mathrm{M}}_{\text{IGM}}$ is described through probability distribution function, $p_{\text{IGM}}(\mathrm{\Delta })$ (Macquart et al., 2020; Miralda-Escude et al., 2000; Zhao et al., 2024), as shown in Equation 11

$p_{\text{IGM}}\left(\mathrm{\Delta }\right)=A{\mathrm{\Delta }}^{-\beta }\exp \left(-\frac{{\left({\mathrm{\Delta }}^{-\alpha }-C_0\right)}^2}{2{\alpha }^2{\sigma }_{\text{DM}}^2}\right),\mathrm{\Delta }>0,(11)$

where $\mathrm{\Delta }\equiv {\mathrm{D}\mathrm{M}}_{\text{IGM}}/⟨{\mathrm{D}\mathrm{M}}_{\text{IGM}}⟩$, and $A$ is a normalization constant. The choice of parameters $\alpha =3$ and $\beta =3$ yields the best agreement with existing models (Macquart et al., 2020). We use the values reported in Table 1 of (Zhang et al., 2021).

Table 1

Table 1. Value of $H_0$ in the different methods using 100 mocks catalogs with 500 synthetic data each.

3 Calculating $H_0$ with our FRB catalog

This section presents three methods for estimating $H_0$ using localizated FRB data in Supplementary Table 2 with 98 entries of these transient events. FRB221027A is excluded for its ambiguity in host galaxy localization, so we perform the calculations of our analysis with a sample of 97 FRBs. In the first method, the median value obtained for $H_0$ is based on the sensitivity of the IGM term to this parameter. The second method focuses on maximizing the likelihood function, while the third one derives from an expression for the cosmic expansion history, $H(z)$, and evaluates it at $z=0$.

3.1 $H_0$ derived with bootstrap and median

The bootstrap method was chosen for its non-parametric nature that shows several general advantages: it estimates uncertainties and confidence intervals without assuming any specific underlying distribution, it naturally propagates parameter correlations across resampled realizations, provides robust estimates for non-linear statistics, and remains reliable for moderately correlated datasets. In particular, for our case: the bootstrap provides a flexible framework where variations in input parameters are automatically propagated through the resampling process, capturing their collective impact on the inferred value of $H_0$. Our bootstrap analysis is structured around a main loop that iterates $N_{\text{BOOT}}=10000$ times. This large number of iterations ensures a stable and well-sampled empirical distribution of $H_0$ estimates, thereby providing reliable confidence intervals. The methodology is specified below.

Within each of the $N_{\text{BOOT}}$ iterations, two steps are performed to ensure that all relevant uncertainties are propagated through the $H_0$ calculation:

• Resampling of Observational Data and Perturbation of Parameters: The ${\mathrm{D}\mathrm{M}}_{\text{tot}}$ and $z$ data are resampled with replacement by adding Gaussian noise to each data point associated with its errors ${\sigma }_{{\text{DM}}_{\text{tot}}}$ and ${\sigma }_z$, respectively. Othe other hand, the constants $f_{\text{IGM}}$, ${\chi }_e$ and ${\mathrm{\Omega }}_b{h}^2$ are perturbed independently from Gaussian distributions defined by their reported values and uncertainties, while ${\mathrm{D}\mathrm{M}}_{\text{MW}}$ and ${\mathrm{D}\mathrm{M}}_{\text{host}}$ are treated as described in the previous section.

• $H_0$ calculation: For each iteration, we have 97 resampled and perturbed data. For each dataset, we use Equation 7 to calculate $H_0$. To this purpose, we substitute each contribution to DM discussed in Section 2 into Equation 3, such that:

${\text{DM}}_{\text{obs}}=\frac{3c{\chi }_e{f}_{\text{IGM}}\cdot 10^4{\mathrm{\Omega }}_b{h}^2}{8\pi G{m}_p{H}_0}{\int }_0^z\frac{1+z^{\prime }}{E\left(z^{\prime }\right)}d{z}^{\prime }+{\text{DM}}_{\text{MW}}+\frac{{\text{DM}}_{\text{host}}}{1+z}.(12)$

From Equation 12, $H_0$ can be written as:

$H_0=\frac{3c{\chi }_e{f}_{\text{IGM}}}{8\pi G{m}_p}\frac{10^4{\mathrm{\Omega }}_b{h}^2}{{\text{DM}}_{\text{obs}}-{\text{DM}}_{\text{MW}}-\frac{{\text{DM}}_{\text{host}}}{1+z}}{\int }_0^z\frac{1+z^{\prime }}{E\left(z^{\prime }\right)}d{z}^{\prime }.(13)$

where, we assume ${\mathrm{\Omega }}_b{h}^2=0.02235\pm 0.00037$ (Hagstotz et al., 2022). The integral is calculated numerically, using the quad function of the scipy.integrate module.

At each bootstrap iteration, we use all 97 resampled/perturbed FRBs to compute 97 individual $H_0$ estimates (discarding any non-physical negative values) and store their median. Repeating this for $N_{\text{BOOT}}=10000$ iterations yields 10000 median $H_0$ values. The median is chosen as a robust estimator, less sensitive to outliers than the statistical mean. This choice is further supported by the asymmetry observed in the distribution of $H_0$ (see Figure 2), which makes the mean more sensitive to outliers. The final estimate of $H_0$ is obtained from the distribution of the $N_{\text{BOOT}}$ medians. The overall median is taken as the best estimate, and the uncertainties are defined using the 16th and 84th percentiles.

Figure 2

Figure 2. The histogram represents the frequency distribution of the medians of the $H_0$ values derived from the bootstrap method for 10000 resamples. The obtained value is $H_0=66.80_{-7.93}^{+8.05}\text{\hspace{0.17em}km/s/Mpc}$. The median and the errors calculated with the 16th and 84th percentiles are shown with red dashed and gray dotted lines, respectively.

Figure 2 displays the result of the mentioned procedure and the associated 16th and 84th percentile errors. The value of $H_0$ obtained by applying the Equation 13 using this method is:

$H_0=66.80_{-7.93}^{+8.05}\text{\hspace{0.17em}km/s/Mpc}.(14)$

If the sample is restricted to $z\le 0.5$, we obtain a value for $H_0=65.77_{-8.34}^{+9.14}\text{\hspace{0.17em}km/s/Mpc}$. Thus, this method shows little sensitivity to the restriction in $z$ due to the large number of resamples being taken.

3.2 $H_0$ from Maximum Likelihood Estimate (MLE) with empirical likelihood

In this section, we estimate the Hubble constant $H_0$ using the Maximum Likelihood Estimation method, taking into account that both ${\mathrm{D}\mathrm{M}}_{\mathrm{I}\mathrm{G}\mathrm{M}}$ and ${\mathrm{D}\mathrm{M}}_{\text{host}}$ follow the non-Gaussian and asymmetric distributions discussed in Section 2. In this case it is not possible to express the likelihood function in closed analytical form, we estimate it empirically using $100000=1000\times 100$ bootstrap realizations of the data. The procedure involves the following steps:

• Define the Likelihood Function: The total likelihood is defined as the product of the conditional probabilities for each observed FRB:

$\mathcal{L}\left(\theta \right)={\displaystyle \prod _{i=1}^{N_{\text{FRB}}}}p\left({\mathrm{D}\mathrm{M}}_{\text{obs},i}\mid \theta \right),(15)$

where $\theta =\{H_0,f_{\text{IGM}},{\chi }_e,{\mathrm{\Omega }}_b{h}^2\}$ denotes the set of physical parameters and $N_{\mathit{FRB}}=97$.

• Generate Synthetic Realizations: For each FRB and for each set of parameters $\theta$, we generate a ensemble of $N_{\text{DM}}=1000$ total dispersion measures:

${\mathrm{D}\mathrm{M}}_{\text{tot},i}^{\left(j\right)}={\mathrm{D}\mathrm{M}}_{\text{MW},i}^{\left(j\right)}+{\mathrm{D}\mathrm{M}}_{\text{host},i}^{\left(j\right)}+{\mathrm{D}\mathrm{M}}_{\text{IGM},i}^{\left(j\right)},(16)$

by sampling ${\mathrm{D}\mathrm{M}}_{\text{host}}$, ${\mathrm{D}\mathrm{M}}_{\text{IGM}}$ and ${\mathrm{D}\mathrm{M}}_{\text{MW}}$ as we mentioned in Section 2.

• The probability density for each observed FRB in Equation 15 is approximated using histogram-based binning around the observed value, as shown in Equation 17

$p\left({\mathrm{D}\mathrm{M}}_{\text{obs},i}\mid \theta \right)\approx \frac{1}{N_{\text{DM}}}{\displaystyle \sum _{j=1}^{N_{\text{DM}}}}{\delta }_{ϵ}\left({\mathrm{D}\mathrm{M}}_{\text{obs},i}-{\mathrm{D}\mathrm{M}}_{\text{tot},i}^{\left(j\right)}\right),(17)$

where ${\delta }_{ϵ}$ is a binning function with bin width $ϵ$ and ${\mathrm{D}\mathrm{M}}_{\text{tot},i}^{\left(j\right)}$ is defined in Equation 16.

• Averaging Over Realizations: For each value of $H_0$ in the grid, we generate $N_{\text{PAR}}=100$ independent realizations of the physical parameters $f_{\text{IGM}},{\chi }_e,{\mathrm{\Omega }}_b{h}^2$ and compute the corresponding log-likelihoods. We then calculate the average log-likelihood from Equation 15 in these realizations as:

$\overline{\ln \mathcal{L}}\left(H_0\right)=\frac{1}{N_{\text{PAR}}}{\displaystyle \sum _{k=1}^{N_{\text{PAR}}}}\ln {\mathcal{L}}_k\left(H_0\right).(18)$

• To reduce fluctuations caused by the empirical approach, we apply a cubic spline interpolation to smooth the average log-likelihood curve obtained from applying Equation 18. We use a third-degree univariate spline and a fixed smoothing factor set to $s=10^8$. This value was chosen after inspecting and comparing different smoothing levels. The final result captures the general trend of the data without being overly sensitive to local variations. The smoothed likelihood is obtained by exponentiating:

${\mathcal{L}}_{\text{smooth}}\left(H_0\right)=\exp \left[{\left(\ln \mathcal{L}\right)}_{\text{smooth}}-\underset{H_0}{\max }{\left(\ln \mathcal{L}\right)}_{\text{smooth}}\right],(19)$

In Equation 19 ${\mathcal{L}}_{smooth}$ was normalized for numerical stability.

• Determination of $H_0$ and its Uncertainty: The peak of this curve provides the best estimate of $H_0$:

$H_0^{\text{MLE}}=\arg \underset{H_0}{\max }\left\{{\mathcal{L}}_{\text{smooth}}\left(H_0\right)\right\}(20)$

The uncertainties are computed from the 16th and 84th percentiles of the final likelihood.

Figure 3 shows the log-likelihood curves from 100 realizations (gray), with their average overlaid in dark red.

Figure 3

Figure 3. Log-likelihood $\ln \mathcal{L}(H_0)$ for 100 realizations (gray) and their mean curve (dark red). The individual peaks are approximately uniformly distributed across the band around $H_0$ and show no prominent secondary maxima. The average curve is smooth and unimodal, with its maximum located where the gray profiles overlap most. A tail asymmetry–already present in several individual curves–motivates reporting asymmetric uncertainties (16th–84th percentiles) and quoting the median as the point estimate.

The 100 individual log-likelihood curves behave very consistently: the peaks are approximately uniformly distributed across the band around $H_0$, with no prominent secondary maxima. The dark red curve -constructed as an average-is smooth and unimodal, and its maximum is located right in the region where the gray curves overlap the most. The distribution of the gray curves about the dark red one indicates that this captures the typical behavior of the sample rather than a few dominant ones. A tail asymmetry is observed (already present in several individual curves), which naturally motivates reporting asymmetric uncertainties (percentiles 16–84) and using the median as an estimator. Finally, in Figure 4, we present the likelihood curve from the dark red curve in Figure 3. The obtained value from Equation 20 for the Hubble constant is:

$H_0^{\text{MLE}}=70.10_{-3.63}^{+4.19}\text{\hspace{0.17em}km/s/Mpc},(21)$

Figure 4

Figure 4. Likelihood for the Hubble constant $H_0$, obtained from 97 localized FRBs using the Maximum Likelihood Estimation (MLE) method. The solid black curve shows the normalized smoothed likelihood, the red dashed line marks the Maximum Likelihood Estimate (MLE) at $H_0=70.10_{-3.63}^{+4.19}\text{\hspace{0.17em}km/s/Mpc}$, and the dotted gray lines indicate the 16th and 84th percentiles corresponding to the 1$\sigma$ uncertainty range.

When we restrict the data to $z\le 0.5$, we obtain a smaller value for this cosmological parameter (with errors of the same order) as when the complete catalog is used, $H_0^{\text{MLE}}=71.17_{-4.25}^{+5.32}\text{\hspace{0.17em}km/s/Mpc}$.

3.3 $H_0$ from cosmic expansion history

In this section, we discuss and apply a method to reconstruct the cosmic expansion history through the Hubble parameter $H(z)$ and estimate its value today, i.e., $H_0$. We remind the reader that we use the sample of localized FRBs in Supplementary Table 2, and models first introduced in (Piratova-Moreno and García, 2024).

The Hubble parameter, the redshift and the mean dispersion measure of IGM for FRBs are interrelated by Equation 10. We obtain an explicit expression for $H(z)$ by deriving that expression with respect to $z$ -following the method shown in (Fortunato et al., 2024).

$H\left(z\right)=\frac{3c\cdot 10^4{\mathrm{\Omega }}_b{h}^2}{8\pi G{m}_p}{\chi }_e{f}_{\mathrm{I}\mathrm{G}\mathrm{M}}\left(1+z\right){\left(\frac{d⟨{\mathrm{D}\mathrm{M}}_{\mathrm{I}\mathrm{G}\mathrm{M}}⟩}{dz}\right)}^{-1}.(22)$

Equation 22 can be used to reconstruct the cosmic expansion history, $H(z)$, computing the derivative of ${\text{DM}}_{\text{IGM}}$ with respect to $z$ and using the latter to estimate $H_0$ as shown in (Liu et al., 2023) and more recently, in (Fortunato et al., 2024). The models presented in (Piratova-Moreno and García, 2024) were originally constrained with 24 known FRBs (at the moment); however, they have updated our current sample of 97 FRBs in Supplementary Table 2. Among the models originally discussed in (Piratova-Moreno and García, 2024), only two have been considered in this work due to their superior performance when predicting $z$ from the observed DM: the linear and power-law models. From Equation 3, ${\text{DM}}_{\text{IGM}}$ is given by:

${\text{DM}}_{\text{IGM}}={\text{DM}}_{\text{obs}}-{\text{DM}}_{\text{MW}}-\frac{{\text{DM}}_{\text{host}}}{1+z}(23)$

If the relationship between ${\text{DM}}_{\text{obs}}$ and $z$ is linear, as the Macquart relation (Macquart et al., 2020; Piratova-Moreno and García, 2024):

${\text{DM}}_{\text{obs}}=az+b,(24)$

with our sample of 97 FRB data points, the best fit parameters for the linear trend are: $a=959.32\pm 73.12\text{pc} {\mathrm{c}\mathrm{m}}^{-3}$ and $b=240.11\pm 25.67\text{pc} {\mathrm{c}\mathrm{m}}^{-3}$, with a coefficient of determination $R^2=0.64$.

Now, if the DM-$z$ relationship is a power-law function (Piratova-Moreno and García, 2024), ${\text{DM}}_{\text{obs}}$ is modeled as:

${\text{DM}}_{\text{obs}}=A{\left(1+z\right)}^{\alpha }.(25)$

The updated values of $A$ and $\alpha$ computed with our 97 localized FRBs are: $A=297.25\pm 17.90\text{pc} {\mathrm{c}\mathrm{m}}^{-3}$, and $\alpha =2.03\pm 0.13$, with a coefficient of determination $R^2=0.64$.

We take the errors on the linear $(a,b)$ and power-law $(A,\alpha )$ fits from the covariance matrices returned by the least-squares routines (polyfit for the linear model; curve_fit for the power law). In this section, we denote the parameter errors by $\mathit{\sigma }$ and the optimal parameter values by $\mathit{\theta }$.

Using the relationships Equations 24, 25 and the updated values for the free parameters in each case, the derivative $\frac{d⟨{\text{DM}}_{\text{IGM}}⟩}{dz}$ can be obtained with Equation 23 and substituted into the Equation 22. The Hubble parameter with our linear model is given by:

$\frac{H\left(z\right)}{1+z}=\frac{3c\cdot 10^4{\mathrm{\Omega }}_b{h}^2}{8\pi G{m}_p}{f}_{\text{IGM}}{\chi }_e{\left[959.32+\frac{100}{{\left(1+z\right)}^2}\right]}^{-1},(26)$

and, equivalently, for our power-law function:

$\frac{H\left(z\right)}{1+z}=\frac{3c\cdot 10^4{\mathrm{\Omega }}_b{h}^2}{8\pi G{m}_p}{f}_{\text{IGM}}{\chi }_e{\left[604.48{\left(1+z\right)}^{1.03}+\frac{100}{{\left(1+z\right)}^2}\right]}^{-1}(27)$

Setting $z=0$ in Equations 26, 27, we recover a value for the Hubble constant:

$H_0=53.03_{-3.42}^{+3.93}\text{km/s/Mpc}\text{for the linear model,}(28)$

and

$H_0=79.75_{-7.91}^{+9.20}\text{km/s/Mpc}\text{for the power}-\text{law function,}(29)$

with statistical precisions of 7.4% and 11.5%, respectively. To estimate errors reported, we construct two additional DM–$z$ curves by shifting the optimal parameter values element-wise by $\pm \mathit{\sigma }$: upper $=\mathit{\theta }+\mathit{\sigma }$, lower $=\mathit{\theta }-\mathit{\sigma }$. For each curve we apply exactly the same shown: compute $⟨{\mathrm{D}\mathrm{M}}_{\text{IGM}}⟩$, take its redshift derivative, insert it into Equation 22, and evaluate at $z=0$, thus obtaining $H_0^{\text{sup}}$ and $H_0^{\text{inf}}$. We define asymmetric uncertainties as $\mathrm{\Delta }{H}_0^{+}=H_0^{\text{sup}}-H_0$ and $\mathrm{\Delta }{H}_0^{-}=H_0-H_0^{\text{inf}}$; we then reported the result as $H_{\mathrm{\Delta }{H}_0^{-}}^{\mathrm{\Delta }{H}_0^{+}}$.

When estimating $H_0$ using the equations derived from the redshift derivative of ${\mathrm{D}\mathrm{M}}_{\text{IGM}}$, a clear difference arises between the models considered. The linear model, physically motivated and expected to be valid at low redshift, yields a value of $H_0=53.03_{-3.42}^{+3.93}$ km/s/Mpc when using the full catalog (with 97 well-localized FRBs). This result is significantly lower than the current estimates (Aver et al., 2015; Riess et al., 2022), and disagrees with both within the error bars. However, when the analysis is restricted to confirmed FRBs with $z\le 0.5$, the linear model produces $H_0=61.47_{-8.05}^{+10.90}$ km/s/Mpc, effectively showing the large impact that the inclusion of intermediate values of $z$ has on this model according to its formulation.

On the other hand, the power-law model, motivated by cosmological simulations accounting for host galaxy evolution, shows a more stable estimate: $H_0=79.75_{-7.91}^{+9.20}$ km/s/Mpc for the full catalog and $H_0=79.89_{-16.45}^{+23.64}$ km/s/Mpc when restricted to FRBs at $z\le 0.5$. This stability in our results suggests that the reconstruction method applied to the power-law function is less sensitive to the inclusion of high redshift sources, possibly because this functional form captures not only the growth in dispersion measure but also additional evolutionary effects.

On the other hand, both the linear and the power-law DM–$z$ fits yield $R^2\approx 0.64$, indicating that they explain the same fraction ($\approx$64%) of the variance in ${\mathrm{D}\mathrm{M}}_{\text{obs}}$. Because the $R^2$ values are indistinguishable, goodness-of-fit in the DM–$z$ plane alone does not discriminate between models. Differences arise only after propagating each fit through the derivative-based reconstruction in Equation 22: the linear form—adequate at low redshift—proves more sensitive to curvature at intermediate $z$, leading to a lower $H_0$ for the full catalog, whereas the power-law, by allowing mild redshift evolution in $⟨{\mathrm{D}\mathrm{M}}_{\text{IGM}}⟩$, yields a more stable $H_0$ under redshift cuts and a more robust reconstruction of $H(z)$.

In summary, these two models lead to different predictions: the linear model tends to underestimate $H_0$ when using the complete data set, due to its simple functional form and its sensitivity to events beyond its expected regime of validity. It is worth mentioning that when first exploring this functional form by (Macquart et al., 2020), their highest $z$ in their sample of 12 localized FRBs reached $\sim$0.6. In contrast, the power-law model, being a more general version of the linear relation, allows for greater flexibility in the derivative of ${\mathrm{D}\mathrm{M}}_{\text{IGM}}$ and better reconstructs $H(z)$, even with distant FRBs. Besides that, the hydrodynamical simulations used to compute the best fits of the power-law function take into account distinct regimes of the IGM and different galaxy populations. Therefore, the power-law function is expected to respond more effectively across various $z$ ranges.

Finally, Supplementary Appendix 3 shows a modification of this method, in which we incorporate observational uncertainties and parameter variability through a bootstrap resampling procedure. In addition, the method applies the cubic spline technique to reduce noise amplification during the differentiation process, with an updated value of $H_0=71.33_{-9.13}^{+8.97}\text{\hspace{0.17em}km/s/Mpc}$. We found that the errors through this method are of the same order as those shown in this section, and the value is close to that presented in Equation 29 with the power-law model, showing the consistency and robustness of our result. The findings of this section can be compared with those obtained by (Liu et al., 2023), who for 64 FRBs evaluate the derivative iteratively through Markov Chain Monte Carlo method. They reported a value of $H_0=71\pm 3\text{\hspace{0.17em}km/s/Mpc}$, similar to our result $H_0=71.33_{-9.13}^{+8.97}\text{\hspace{0.17em}km/s/Mpc}$ obtained with bootstrap and splines but with a significantly lower error Equation 34 in Supplementary Appendix 3.

The results obtained through the three methods with observed (and confirmed) FBRs are presented in Figure 5.

Figure 5

Figure 5. Estimates of the Hubble constant $H_0$ obtained using different methods: Median (Equation 14) and Maximum Likelihood Estimation (MLE) (Equation 21) and H(z) reconstruction with linear (Equation 28) and power-law (Equation 29) models. The vertical grey bands represent the values reported by Planck et al., 2020; Riess et al., 2022).

Figure 5 shows the current scenario for $H_0$ values, computed with different methods explored in this study. While some schemes, such as the reconstruction of $H(z)$ with the linear model, yield lower values than those reported in the literature, that same reconstruction using a power-law model produces higher estimates than the most accepted references. Additionally, some methods–such as the median–yield values that, within their error bars, are compatible with both values reported in the literature by (Riess et al., 2022; Hagstotz et al., 2022).

4 Future prospectives with FRBs mock data

Currently, the available set of confirmed FRBs is limited; however, it is possible to simulate data to gain insight into the potential of these statistical and numerical methods. Following the procedure proposed in (Liu et al., 2023; Fortunato et al., 2024; Yu and Wang, 2017), we adopt a flat $\mathrm{\Lambda }$CDM model as the fiducial model, with the following cosmological parameters: $H_0=70\text{\hspace{0.17em}km/s/Mpc}$, ${\mathrm{\Omega }}_b=0.049$, ${\mathrm{\Omega }}_m=0.3$, and ${\mathrm{\Omega }}_{\mathrm{\Lambda }}=1-{\mathrm{\Omega }}_m$. Furthermore, we assume that the redshift distribution is described by $f(z)\approx z^2\exp (-\alpha z)$, with $\alpha =7$ -following the galaxy distribution presented by (Hagstotz et al., 2022), a parameter that determines the depth of the simulated sample, acting as a filter that places most of the data points within the range $z=0.15-0.5$ consistent with confirmed data to-date.

The ${\text{DM}}_{\text{IGM}}$ term is proposed through a normal distribution $N(⟨{\text{DM}}_{\text{IGM}}^{\text{fid}}⟩,{\sigma }_{{\text{DM}}_{\text{IGM}}^{\text{fid}}})$, where ${\sigma }_{{\text{DM}}_{\text{IGM}}^{\text{fid}}}={\sigma }_{\mathrm{\Delta }\text{IGM}}(z)$, as shown in Equation 30. The term $⟨{\text{DM}}_{\text{IGM}}^{\text{fid}}⟩$ is calculated in Equation 10. The large dispersion of the values of ${\text{DM}}_{\text{IGM}}$ around its mean value $⟨{\text{DM}}_{\text{IGM}}⟩$ is due to the inhomogeneity of the distribution of baryons in the intergalactic medium is modeled by with a power-law function presented in (Rajwade and Leeuwen, 2024; Hunter, 2007; Qiang and Wei, 2020):

${\sigma }_{\mathrm{\Delta }\text{IGM}}\left(z\right)=173.8z^{0.4}\text{\hspace{0.17em}pc\hspace{0.17em}}{\text{cm}}^{-3}.(30)$

The contribution of the host galaxy is described by a log-normal distribution, as shown in the Equation 31

$P\left({\text{DM}}_{\text{host}}\right)=\frac{1}{{\text{DM}}_{\text{host}}{\sigma }_{\text{host}}\sqrt{2\pi }}\exp \left(-\frac{{\ln }^2\left({\text{DM}}_{\text{host}}/\mu \right)}{2{\sigma }_{\text{host}}^2}\right).(31)$

Here, $\mu$ is the geometric mean, and we consider it within the range $[\mathrm{40,80}]{\text{pc cm}}^{-3}$. The term ${\sigma }_{\text{host}}$ is within the interval $[0.4,1.0]$.

We generate 100 independent realizations from random seeds between 0 and 199. Each set contains 500 simulated FRBs. We display one example of these synthetic samples in Figure 6. For each realization, we calculate a value of $H_0$ applying the methods described in previous sections, such that we recover a set of 100 different values for $H_0$. Finally, we calculate the median and the associated 16th and 84th percentile errors for all these $H_0$ values, which yields the results shown in Table 1.

Figure 6

Figure 6. Simulated sample of 500 FRBs generated under a flat cosmological model. The redshift distribution follows $f(z)\propto z^2\exp (-\alpha z)$. The total dispersion measure $(\mathrm{D}\mathrm{M})$ includes contributions from the intergalactic medium (IGM), modeled as a normal distribution, a host galaxy term modeled using a log-normal distribution and constant contribution from Milky way. This Figure shows one of the 100 realizations used to statistically recover $H_0$ from the synthetic data.

Notably, our findings using the median-bootstrap method, both for the bootstrap scheme with the 97 confirmed FRBs and the synthetic catalogs presented in this section, are highly consistent, demonstrating that implementing a large number of subsamples of the real data works effectively as creating simulated transients and leads to equivalent results, $H_0=66.80_{-7.93}^{+8.05}\text{\hspace{0.17em}km/s/Mpc}$ and $66.10_{-2.50}^{+2.42}\text{\hspace{0.17em}km/s/Mpc}$, for the observed and synthetic samples, respectively.

The statistical precision will continue to improve as more confirmed data become available. The best performance is achieved through the implementation of the MLE method, with values from $70.10_{-3.63}^{+4.19}\text{\hspace{0.17em}km/s/Mpc}$ (statistical precision $\sim$6.0%) calculated with the 97 FRBs in Supplementary Table 2 and $67.30_{-0.85}^{+0.98}\text{\hspace{0.17em}km/s/Mpc}$ (statistical precision 1.5%) for our synthetic dataset. In summary, the statistical precision improves by a factor of four when new data is used as input in our calculations, and in the mock case, under the assumptions underlying our data-generating process and the limitations of the current sample, the resulting precision rises to a level comparable to that reported by the SH0ES collaboration. On the other hand, methods based on the reconstruction of $H(z)$ exhibit the largest deviations from the values reported in (Riess et al., 2022; Hagstotz et al., 2022). Notably, our prediction with the median value has a statistical precision similar to the methods based on $H(z)$, and it is compatible with the value of $H_0$ reported by (Riess et al., 2022).

5 Conclusion

The Hubble constant $(H_0)$ is a very important cosmological parameter that measures the rate of expansion of the universe today. The so-called “Hubble tension” is the discrepancy with a gap of more than $5\sigma$ between the predictions of $H_0$ values by early (Aver et al., 2015) and late universe (Riess et al., 2022) observations. Fast radio bursts (FRBs) offer new pathways to quantify this cosmological parameter. In particular, it can be used to address the Hubble tension based on the sensitivity of the dispersion measure, in particular, in the IGM term. We construct a data set with 98 localized FRBs from literature and explore three different methods to estimate $H_0$ value with 97 of them: i) median-bootstrap, ii) the Maximum Likelihood Estimate and iii) reconstruction of $H(z)$.

In the first method, based on the sensitivity of the intergalactic medium dispersion measure $({\text{DM}}_{\text{IGM}})$ to the Hubble constant, $H_0$ is estimated as median of a distribution of 10000 values obtained by a bootstrap method. Using the data from Supplementary Tables 2, 3, we generate perturbed datasets as follows: we perform a bootstrap of 10000 resamples with replacement, in which Gaussian noise is included for $f_{\text{IGM}}$, ${\chi }_e$ and ${\mathrm{\Omega }}_b{h}^2$, while non-Gaussian distributions for ${\mathrm{D}\mathrm{M}}_{\text{host}}$ and ${\mathrm{D}\mathrm{M}}_{\text{IGM}}$ are adopted; in addition, the NE2001 model is assumed with Gaussian noise around its predicted values for ${\mathrm{D}\mathrm{M}}_{\text{MW}}$. As a robust estimator of $H_0$, we take the median of the mentioned distribution, and its errors are calculated from the 16th and 84th percentiles, obtaining $H_0=66.80_{-7.93}^{+8.05}\text{\hspace{0.17em}km/s/Mpc}$, with a statistical precision of 12.1%. This result shows agreement with reports from (Riess et al., 2022).

In the second method, we use the MLE method to determine the best value of $H_0$ that fits the proposed model to the 97 localized FRBs. This method achieves the best statistical precision at 6.0%, predicting a value for the Hubble parameter today of $H_0=70.10_{-3.63}^{+4.19}\text{\hspace{0.17em}km/s/Mpc}$. The latter result with 97 confirmed FRBs is quite encouraging, since it reflects that our assumption of using FRBs as cosmological proxies is an exceptional opportunity to alleviate the Hubble tension, with a value that lies right in between reports from (Riess et al., 2022; Hagstotz et al., 2022).

Finally, the cosmic expansion history $H(z)$ is reconstructed by taking the derivative of the average value ${\text{DM}}_{\text{IGM}}$ with respect to $z$. Two DM-$z$ relations are considered for calculating the derivative: linear and power-law functions. These relationships are fitted using the 97 confirmed data points. Once $H(z)$ is reconstructed, we set $z=0$ to recover $H_0$. The linear function leads to a value of $H_0$ of $53.03_{-3.42}^{+3.93}\text{\hspace{0.17em}km/s/Mpc}$, closer to reports by (Riess et al., 2022), with a statistical precision of 7.4%. On the other hand, unlike previous results, the power-law model predicts a higher value than (Riess et al., 2022), $79.75_{-7.91}^{+9.20}\text{\hspace{0.17em}km/s/Mpc}$. However, the latter value exhibits lower statistical precision than the linear model, at 11.5% level.

When we restrict the sample to low values of redshift (in our case, $z\le 0.5$), we find that median-bootstrap, the MLE method and H(z) power-Law reconstruction methods show low sensitivity to the restriction, whereas the reconstruction of H(z) through a linear model has a significant impact in the redshift selection of the sample.

Overall, our results with observed FRBs have lower statistical precision compared to (Riess et al., 2022; Aver et al., 2015). However, the number of FRBs with confirmed host galaxies is expected to increase significantly shortly. Therefore, it seems promising to evaluate these methods with larger datasets. To this end, we generate 100 mock catalogs with 500 data points each. We assume a particular redshift distribution discussed in Section 4, a normal distribution for ${\text{DM}}_{\text{IGM}}$ with a standard deviation that depends on redshift and we take a log-normal distribution for the host galaxy dispersion measure and repeat the calculations with the three methods discussed with 500 data points to recover a set of 100 different values for $H_0$. Finally, we calculate median the of the distribution of the $H_0$ values for each method and obtain the following results for $H_0$: $66.10_{-2.50}^{+2.42}\text{\hspace{0.17em}km/s/Mpc}$ (for median method), $67.30_{-0.85}^{+0.98}\text{\hspace{0.17em}km/s/Mpc}$ (with the MLE method), $54.41_{-1.63}^{+1.45}\text{\hspace{0.17em}km/s/Mpc}$ and $91.69_{-1.85}^{+2.08}\text{\hspace{0.17em}km/s/Mpc}$, with the $H(z)$ reconstruction method with a linear and a power-law function, respectively. In all the methods applied to mock data, the statistical precision improves significantly, but the MLE method stands out with a value of 1.5%, which is comparable to the reports by (Riess et al., 2022).

Besides the values reported for $H_0$ with the different methods explored in this work, we highlight that the statistical precision of the predicted value of $H_0$ increases by a factor of four if the set of confirmed (and localized) FRBs grows at least 5 times the current sample. More importantly, our results are partially consistent with other indirect methods for inferring the Hubble factor today, as the main observable considered here, the dispersion measure (DM), effectively represents the distance between the observer and the FRB. Hence, it is unsurprising that most of our predictions fall within the range of values predicted by other indirect methods, such as CMB or BAO. Although our sample of FRBs remains in a low redshift regime ($z_{\text{high}}\sim$ 1.3), our results are more compatible with predictions of $H_0$ derived with early universe probes than forecasts of this cosmological parameter made with observations in the local universe. Nonetheless, it is remarkable that with a non-parametric statistical method and our sample of about a hundred FRBs, the derived value of the $H_0$ lies between (Aver et al., 2015) and (Riess et al., 2022), alleviating the current Hubble tension, exactly the reason that motivated this study.

Finally, with a growing census of well-localized FRBs, new programs and statistical schemes would improve our current estimates for the Hubble constant (and their statistical significance) and other relevant cosmological parameters.

Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

Author contributions

EP-M: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. LG: Conceptualization, Data curation, Formal Analysis, Investigation, Methodology, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing. CB-G: Writing – review and editing. AC: Writing – review and editing.

Funding

The author(s) declare that financial support was received for the research and/or publication of this article. This work was supported by Fundación Universitaria Los Libertadores programme “Décimo Segunda (XII) Convocatoria Interna Anual de Proyectos de Investigación, Creación Artística y Cultural”, project “Estimación del espacio de parámetros para modelos difusivos cosmológicos a través de métodos bayesianos y de machine learning.” [Grant number: ING-14-24]. This material is based upon work supported by the Google Cloud Research Credits program with the award GCP19980904. This research made use of matplotlib (Hunter, 2007), Scipy (Virtanen et al., 2020) and Numpy (Harris et al., 2020).

Acknowledgements

The authors thank Fundación Universitaria Los Libertadores and Universidad ECCI for granting us the resources to develop this project.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The author(s) declare that no Generative AI was used in the creation of this manuscript.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fspas.2025.1573311/full#supplementary-material

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