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Crisis in cosmology? Or just tweaking models?
(lemmy.world)
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The video (you can skip to the last five or 10 minutes of it to get the gist of what I'm talking about) says that the discrepancy isn't unexplained. It's point is that the different models depend on a large number of variables, and one of those variables is the size and brightness of the first generation of stars in the early universe. Tweaking that part of the model can explain the discrepancy. (According to the video.)
OK, I've actually watched the video this time (the last part, as you suggested). It seems that the author decided to leave out the debate about the Hubble constant and talk about other phenomena in the early universe, which also have their uncertainties.
As far as I can tell, the Hubble tension is still a thing, and JWST only confirmed the measurements of the Hubble telescope. See for example this recent article on ars technica.