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

We consider constraints on the Hubble parameter (Formula presented.) and the matter density parameter (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) (the ‘Hubble tension’), which can only be reconciled with the age constraint at an implausibly low (Formula presented.). We suggest instead that outflow from the local KBC supervoid inflates redshifts in the nearby universe and, thus, the apparent local (Formula presented.). 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.