The local void model for the Hubble and BAO tensions

TL;DR

The paper investigates the Hubble tension as a predominantly low-redshift phenomenon and evaluates a local void (notably the KBC void) as a solution in which non-cosmological redshift contributions inflate $cz'$ at $z\lesssim0.2$ while preserving $H_0 = H_0^{\mathrm{CMB}}$ at early times. It argues that a large underdensity can generate outward peculiar velocities and a gravitational-redshift term, potentially reconciling the local $cz'$ with CMB-based expansion and offering a natural explanation for the recent BAO anomaly via a declining $D_V/r_d$ at low redshift and convergence to Planck-like values at higher $z$. The authors show that BAO data over the last two decades can be better fit by void models than by a homogeneous Planck cosmology, particularly when past-lightcone GR effects are included; they also discuss how reconstructions of $H_0(z)$ from BAO and uncalibrated SNe Ia align with the void predictions. They outline a range of future tests—galaxy counts, peculiar velocities, FRBs, redshift drift, kSZ measurements, and large-scale structure growth—that could decisively discriminate between a local-void scenario and purely late-time background solutions, with FRBs highlighted as a particularly promising probe. The study highlights the broader significance: if correct, the local void implies modified gravity on >100 Mpc scales and challenges the need for new physics before recombination, offering a tightly constrained, testable pathway to resolving the Hubble and BAO tensions.

Abstract

The inconsistency between the locally inferred Hubble constant and the value inferred from the cosmic microwave background assuming the $Λ$CDM cosmological model has persisted, turning into an important problem. An emergent underlying trend is that this Hubble tension is driven by data confined to the very low-redshift Universe (typically $z < 0.15$). Most intermediate-redshift measurements remain mutually consistent with $H_0^\mathrm{CMB}$, the $Λ$CDM expectation anchored by the CMB. This Perspective examines if a large local void can explain the Hubble tension and its appearance only at low $z$. For an observer residing within a large underdensity, such as the Milky Way inside the claimed KBC void, gravitationally induced outflows and redshift can inflate the locally inferred recession scale $cz'$ despite having $H_0 = H_0^\mathrm{CMB}$. We summarise evidence suggestive of a local underdensity from multi-wavelength galaxy number counts, discuss the dynamical requirements implied by the amplitude of inferred bulk flows, and connect the solution to the emerging low-redshift BAO distance anomaly ($α_{\mathrm{iso}} < 1$). Previously published semi-analytic void models anticipated the observed redshift dependence of BAO deviations and predict a rapid convergence to CMB-consistent expansion for $z \gtrsim 0.2$, aligning with reconstructions of $H_0(z)$ from BAO plus uncalibrated Type Ia supernovae. We conclude by looking to future tests, including improved mapping of the local density and velocity field, fits to galaxy distance catalogues at the field level, kinematic Sunyaev-Zel'dovich constraints on coherent outflows, fast radio bursts, and the long-term prospect of redshift drift measurements as a direct probe of time-varying non-cosmological redshift contributions.

Figures (5)

• Figure 1: Constraints on $h \equiv H_0$ in units of 100 km/s/Mpc and $\Omega_\mathrm{M}$, the fraction of the cosmic critical density presently in the matter component. The solid lines show the most likely values, while the shaded bands show $1\sigma$ uncertainties. The CMB constraint assuming $\Lambda$CDM is shown as the thin grey ellipse with central white star Tristram_2024. The horizontal orange band shows a typical local $cz'$ measurement Said_2025Scolnic_2025. The tension between these two is the Hubble tension. The vertical red band obtains $\Omega_\mathrm{M}$ using uncalibrated BAO data from DESI DR2 DESI_2025. The sloped blue band uses the age of the Universe from old Galactic globular clusters Valcin_2025. The dark blue region assumes the oldest one formed $t_\mathrm{f} = 0.2$ Gyr after the Big Bang, while the light blue band allows $t_\mathrm{f}$ to be $2\times$ smaller or larger. The open black contour uses measurements of LSS and uncalibrated SNe Ia Farren_2025. Notice how the local $H_0$ is the only constraint not consistent with the others. Reproduced from figure 2 of Banik_2025_cosmology.
• Figure 2: BAO measurements of $\alpha_{\mathrm{iso}}$ (Equation \ref{['alpha_iso']}) over the last twenty years, scaled to the prediction in the Planck cosmology. The colour of each point indicates the survey used, while the marker size indicates the year of publication, emphasizing more recent measurements. The $\Lambda$CDM prediction is by definition unity at all $z$, with the approximate uncertainty shown by the shaded grey band. Predictions of the void models are shown with solid coloured lines for different initial underdensity profiles, as indicated in the legend. For illustrative purposes, the dashed lines show the corresponding model predictions without GR (Equation \ref{['z_contributions']}), highlighting its importance. To avoid double counting studies whose observations were later reused in a different study shown here, the points with grey error bars were excluded when quantitatively comparing model predictions to observations. Reproduced from figure 4 of Banik_2025_BAO.
• Figure 3: The cosmic expansion history in different models. The black curve shows the Planck cosmology, while the grey curve shows the CPL model fit to CMB + BAO Mirpoorian_2025. Uncertainties on the $H_0$ predictions of these models are indicated at the left. The lowest horizontal band in magenta shows the predicted $H_0$ in their PMF-inspired model where recombination occurs slightly earlier than in $\Lambda$CDM. The higher horizontal bands show two typical local $cz'$ measurements Breuval_2024Scolnic_2025. The coloured solid curves show predictions in the local void models, as indicated in the legend. The apparent $a$ at any lookback time is obtained from the measured redshift assuming homogeneity (Equation \ref{['a_app']}). The true background $\dot{a}(z)$ in the void models is the solid black curve.
• Figure 4: Predicted $H_0(z)$ curves in the void models and according to observations Jia_2025b. The horizontal blue band at the top shows the local $cz'$ measurement Breuval_2024, while the lower magenta band shows $H_0$ estimated from old Galactic stars and stellar populations Cimatti_2023. The horizontal olive line shows $H_0^\mathrm{CMB}$, with uncertainty indicated at the left Camphuis_2025. The solid curves show void model predictions Mazurenko_2025. For illustrative purposes, the dashed red curve shows the prediction of the Gaussian model without including GR (Equation \ref{['z_contributions']}). Its importance is clear from comparison with the solid red curve. The square points with uncertainties are based on a flexible reconstruction of the expansion history using BAO + uncalibrated SNe Ia from Pantheon+ (black) or DES Y5 (green). The horizontal uncertainties indicate the redshift range of each bin Jia_2025b. Adapted from figure 3 of Mazurenko_2025.
• Figure 5: The forecasted redshift drift $\Delta z$ over a decade in different cosmological models. The solid black line in the left panel shows the homogeneous Planck cosmology, which is subtracted from the other models in the right panel to highlight differences. The coloured curves slightly above it show predictions in the void models Haslbauer_2020. The low grey curve shows the CPL model fit to Planck CMB + BAO Mirpoorian_2025.