- Review
Constraints on the Hubble and Matter Density Parameters with and Without Modelling the CMB Anisotropies
- Indranil Banik and
- Nick Samaras
We consider constraints on the Hubble parameter and the matter density parameter from the following: (i) the age of the Universe based on old stars and stellar populations in the Galactic disc and halo; (ii) the turnover scale in the matter power spectrum, which tells us the cosmological horizon at the epoch of matter-radiation equality; 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). A narrow region is consistent with all three constraints just outside their 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 (the ‘Hubble tension’), which can only be reconciled with the age constraint at an implausibly low . We suggest instead that outflow from the local KBC supervoid inflates redshifts in the nearby universe and, thus, the apparent local . 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.
19 November 2025


![The
1
σ
constraints on
Ω
M
and
h
≡
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; [33]), the turnover scale in the matter power spectrum (green; [40]), and the ages of old stars in the Galactic disc and halo (blue; [46]), with the light blue band allowing for a factor of 2 uncertainty in their formation time. The grey error ellipse shows the Planck fit to the CMB anisotropies in
Λ
CDM [50], which provide the tightest constraint on the combination
Ω
M
h
3
[51]. 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 [58], with four anchor galaxies used to calibrate the Leavitt Law.](/_ipx/b_%23fff&f_webp&q_100&fit_outside&s_470x317/https://mdpi-res.com/astronomy/astronomy-04-00024/article_deploy/html/images/astronomy-04-00024-g001-550.jpg)