Testing the local supervoid solution to the Hubble tension with direct distance tracers

TL;DR

This work tests the local void explanation for the Hubble tension by forward-modeling three KBC-like void density profiles against direct distance tracers from the CF4 Tully–Fisher sample within a Planck cosmology. Through galaxy-by-galaxy inference, it jointly constrains void parameters (size, observer offset, external velocity) and TFR calibration, revealing a preference for small voids ($\tilde{r}_{\rm void} \sim 0.06$–$0.15$, i.e. roughly $34$–$69$ cMpc) and local $H_0$ values around $70$–$72$ km s$^{-1}$ Mpc$^{-1}$ depending on profile. Bayesian model selection disfavors the exponential profile, while Gaussian and Maxwell–Boltzmann profiles provide better fits but still leave a residual Hubble tension of about $3\sigma$; bulk-flow inferences from CF4 show tension with the Watkins_2023 curve, highlighting potential data or modelling limitations. Overall, the local void remains a plausible, but not definitive, mechanism for easing the Hubble tension, and the results point to the need for more complex void structures and broader, deeper datasets to fully assess this solution.

Abstract

Several observational studies suggest that the local few hundred Mpc around the Local Group are significantly underdense based on source number counts in redshift space across much of the electromagnetic spectrum, particularly in near-infrared galaxy counts. This ``Keenan--Barger--Cowie (KBC) void'', ``Local Hole'', or ``local supervoid'', would have significant ramifications for the Hubble tension by generating outflows that masquerade as an enhanced local expansion rate. We evaluate models for the KBC void capable of resolving the Hubble tension with a background Planck cosmology. We fit these models to direct distances from the Tully--Fisher catalogue of the CosmicFlows-4 compilation using a field-level forward model. Depending on the adopted void density profile, we find the derived velocity fields to prefer a void size of less than 70 Mpc, which is less than 10 per cent of the fiducial size found by Haslbauer et al. based on the KBC luminosity density data. The predicted local Hubble constant is $72.1^{+0.9}_{-0.8}$, $70.4^{+0.4}_{-0.4}$, or $70.2^{+0.5}_{-0.4}$ km/s/Mpc for an initial underdensity profile that is exponential, Gaussian, or Maxwell-Boltzmann, respectively. The latter two ameliorate the Hubble tension to within $3σ$ of the 4-anchor distance ladder approach of Breuval et al. giving $73.2 \pm 0.9$ km/s/Mpc. The exponential profile does achieve consistency with this measurement at just over $1σ$, but it is disfavoured by the Bayesian evidence. The preferred models produce bulk flow curves that disagree with recent estimates from CosmicFlows-4, despite the void models being flexible enough to match such estimates.

Figures (12)

• Figure 1: The distribution of galaxy redshifts in the CMB frame ($z_{\rm obs}$) for the CF4 TFR sample. The upper $x$-axis shows $z_{\rm obs}$ converted to comoving distance assuming no peculiar velocity. The plot shows separately the set of galaxies with $i$-band SDSS photometry and $W1$-band WISE photometry.
• Figure 2: Posterior distributions of the inferred void model parameters obtained by fitting the flow model described in \ref{['sec:flow_model']} to the CF4 TFR data. Results are shown for the exponential (red), Gaussian (blue), and Maxwell-Boltzmann (green) void profiles. The sampled parameters include the magnitude and direction of the external velocity $\bm{V}_{\rm ext}$ in Galactic coordinates, the observer's offset $R_{\rm offset}$ from the void centre along the symmetry axis, the relative void size $\tilde{r}_{\rm void}$, and the velocity scaling parameter $\beta$. For all three profiles, we find a preference for significantly smaller void sizes compared to the fiducial sizes in Haslbauer_2020.
• Figure 3: The inferred void density field (left panel), the outflow velocity curve (i.e., the monopole of the velocity field; middle panel), and the bulk flow curve (an integral of the dipole of the velocity field; right panel) as a function of distance from the observer, using the void parameters and their uncertainties as inferred by our field-level analysis. We show results for the exponential (Gaussian; Maxwell-Boltzmann) profile using red (blue; green) shaded bands, which indicate the $1\sigma$ uncertainty. In the right panel, the dot-dashed lines show $V_{\rm ext}$ and the dotted lines show the bulk flow without including $\bm{V}_{\rm ext}$, i.e., that produced intrinsically by the void. The dashed lines show the bulk flow curves in the models that best fit the results of Watkins_2023, where the colour again indicates the density profile. The Watkins_2023 results themselves are shown as black points with uncertainties.
• Figure 4: Posterior predictive distributions of $H_0^{\rm local}$ when jointly varying the void size and velocity scaling parameter $\beta$ for the exponential, Gaussian, and Maxwell-Boltzmann void profiles (shown in red, blue, and green respectively). We find $H_0^{\rm local} = 72.08^{+0.86}_{-0.80}$, $70.40^{+0.43}_{-0.38}$, and $70.18^{+0.48}_{-0.40}$ km/s/Mpc for the exponential, Gaussian, and Maxwell-Boltzmann profiles, respectively. For comparison, we show the Planck and 4-anchor SH0ES $H_0$Planck_2020Breuval_2024 as unfilled dashed black and solid magenta distributions, respectively. The Planck$H_0$ is the background value assumed by the void models.
• Figure 5: The logarithmic Bayes factor for a grid of void sizes, which we hold fixed during each inference. The Bayes factors are relative to a model where the velocity field is modelled only by a constant dipole $\bm{V}_{\rm ext}$, with positive values indicating a preference over this simple void-free model. While most of the probed range of void sizes is preferred over the simpler pure dipole model with no net outflow, the preference is much stronger for voids significantly smaller than the fiducial size found by Haslbauer_2020. The two preferred models are the Gaussian and Maxwell-Boltzmann profiles with $\tilde{r}_{\rm void} \approx 0.06$ and $0.15$, respectively.