Ryan tells us about how the Hubble tension (between Planck measurements of the cosmic microwave background temperature anisotropies and SH0ES measurements of the expansion rate of the universe) can be completely solved with a non-standard primordial power spectrum for the curvature perturbation, which could arise e.g. if there is a kink in the inflationary potential.

The non-standard power spectrum has an oscillatory feature that exactly mimics the effects of a slightly different value for the expansion rate today. They find this power spectrum by explicitly reconstructing it, so they aren’t supplying a well motivated a priori model. However their work does represent a proof of concept that a non-standard power spectrum could mimic the effects of a different expansion rate.

While the Hubble tension remains unsolved and while all other models to explain it suffer from their own problems, work like this remains well motivated. It would perhaps be a bit fine tuned to have a feature at exactly the right place in the primordial power spectrum to mimic the effects of H0 today, but there could be many features and if one happened to align then this would be what we would see, so it can’t be ruled out a priori.

Future work will test this with polarisation data and the matter power spectrum… so stay tuned. If this is the solution it might leave measurable signatures in those results.

Ryan: http://cosmology.kasi.re.kr/members.php?member=ryan
The paper: https://arxiv.org/abs/2006.12710