Constraints on the Hubble and matter density parameters with and without modelling the CMB anisotropies

TL;DR

The paper investigates constraints on $H_0$ and $Ω_{ m M}$ using non-CMB probes that are insensitive to recombination physics—uncalibrated cosmic standards (UCS), the turnover scale in the matter power spectrum via $k_{ m eq}$, and stellar ages—and compares these to the Planck LCDM constraints. The three non-CMB methods define a narrow region in the $(Ω_{ m M}, h)$ plane that lies just outside their 1σ overlaps but coincides with the Planck 1σ region, arguing against early-time resolutions to the Hubble tension and suggesting late-time or local explanations, such as a local void or expansion-history modifications. The persistent high local $H_0$ from the distance ladder remains the primary outlier, reinforcing the case for late-time physics or inhomogeneity rather than new early-universe dynamics. Overall, the work strengthens the view that solutions to the Hubble tension are unlikely to lie in early-universe modifications and highlights the potential importance of late-time expansion dynamics or local structure.

Abstract

We consider constraints on the Hubble parameter $H_0$ and the matter density parameter $Ω_{\mathrm{M}}$ from: (i) the age of the Universe based on old stars and stellar populations in the Galactic disc and halo (Cimatti & Moresco 2023); (ii) the turnover scale in the matter power spectrum, which tells us the cosmological horizon at the epoch of matter-radiation equality (Philcox et al. 2022); and (iii) the shape of the expansion history from supernovae (SNe) and baryon acoustic oscillations (BAOs) with no absolute calibration of either, a technique known as uncalibrated cosmic standards (UCS; Lin, Chen, & Mack 2021). A narrow region is consistent with all three constraints just outside their $1σ$ uncertainties. Although this region is defined by techniques unrelated to the physics of recombination and the sound horizon then, the standard $Planck$ fit to the CMB anisotropies falls precisely in this region. This concordance argues against early-time explanations for the anomalously high local estimate of $H_0$ (the 'Hubble tension'), which can only be reconciled with the age constraint at an implausibly low $Ω_{\mathrm{M}}$. We suggest instead that outflow from the local KBC supervoid (Keenan, Barger, & Cowie 2013) inflates redshifts in the nearby universe and thus the apparent local $H_0$. Given the difficulties with solutions in the early universe, we argue that the most promising alternative to a local void is a modification to the expansion history at late times, perhaps due to a changing dark energy density.

Figures (3)

• Figure 1: The $1\sigma$ constraints on $\Omega_{\mathrm{M}}$ and $h \equiv H_0$ in units of 100 km/s/Mpc from the shape of the expansion history traced by SNe and BAOs with no absolute calibration of either *[red;][]Lin_2021_UCS, the turnover scale in the matter power spectrum Philcox_2022, and the ages of old stars in the Galactic disc and halo Cimatti_2023, with the light blue band allowing a factor of 2 uncertainty in their formation time. The grey error ellipse shows the Planck fit to the CMB anisotropies in $\Lambda$CDM Tristram_2024, which provide the tightest constraint on the combination $\Omega_{\mathrm{M}} h^3$ *Kable_2019. The white dot at its centre shows the most likely values. The yellow band shows $h$ estimated from the local redshift gradient by the SH0ES team Breuval_2024, with 4 anchor galaxies used to calibrate the Leavitt Law.
• Figure 2: Similar to Figure \ref{['OmegaM_h']}, but using different non-CMB constraints in each case. The shape of the expansion history is constrained using DESI DR2 BAO measurements DESI_2025. The age of the Universe is estimated using Galactic GCs Valcin_2025, with the same assumed formation time. The open black contour shows the constraint from uncalibrated SNe Ia combined with three different 2-point statistics of large-scale structure, namely galaxy-galaxy, galaxy-lensing, and lensing-lensing Farren_2025. The CMB is used as the source radiation, but the constraint largely derives from the clustering properties of matter at late times. This also contains information about the turnover scale in the matter power spectrum, and thus the epoch of matter-radiation equality (see the text). The yellow band shows $h$ estimated from the local redshift gradient using DESI FP measurements Said_2025 calibrated using the distance to the Coma Cluster Scolnic_2025. No measurement of its distance since 1990 exceeds the minimum of 110 Mpc required for consistency with the Planck$\Lambda$CDM constraint.
• Figure 3: Similar to Figure \ref{['OmegaM_h_ACT_SN']}, but with the LSS result Farren_2025 now shown excluding SNe Ia.