Amidst all the talk a year and change ago about the value of the Hubble parameter reached by the Planck satellite team, and how it's value differed from the value reached by the 'distance-ladder' team(s), I've yet to read an explanation of how precise measurement of the cosmic microwave background's 'temperature' fluctuations and E-mode polarization(s) ultimately give you a value for Hubble's 'constant'...
I presume the answer is a bit complicated, or I probably would have found it somewhere...
Also, the Planck satellite shut down or whatever in 2013, and this news came out only last year...
Is it okay to 'edit' this question to put it back at the top?
I still don't have a real answer, and the recent news articles and videos about Wendy Freedman and her attempts to resolve the tensions surrounding the discrepancies in the measurements of Hubble's 'constant' always imply that astrophysicists and cosmologists consider the Planck CMB measurement-based cosmological model to be 'better', more reliable, based on sounder, better-understood science than the distance-ladder method...