Attempting to solve the Hubble tension combining varying electron mass and ΛsCDM

I’m very, very glad to see my latest work with Yo Toda, William Giarè, Emre Özülker, and Eleonora Di Valentino finally out on arXiv after several months of hard work (especially by the first author Yo who did all the heavy lifting)! The idea is motivated by my seven hints paper (see this earlier news item) arguing that solving the Hubble tension may require a combination of pre- and post-recombination new physics, and here we attempted to construct precisely such a combination, focusing on models which individually worked well in the pre- and post-recombination era so far: a spatially uniform time-varying electron mass in a non-spatially flat Universe, and the ΛsCDM model, featuring a late-time sign-switching cosmological constant (from negative to positive). In the end the idea didn’t quite work, but we still decided to document our attempt because we learned a great deal about potential difficulties and drew what we hope are important general lessons for future endeavours: for the record, these are reported between Pages 10 and 13 and, spoiler, Ωm plays a crucial role in explaining why this didn’t work. A fun fact Özgür Akarsu reminded me of is that around minute 44 of my Universe Today Podcast interview with Fraser Cain back in November (see this earlier news item) I actually gave a very detailed spoiler of this project, as I had spoken to Yo a few days back so we had just gotten it started (and I had quite high hopes on this working out, which it certainly did in the sense of learning a whole lot of new things, although not in the way I initially expected). You can read our results in the preprint we just posted on arXiv: 2407.01173.