I bookmarked this paper on arXiv a week or so ago with the intention of sharing it here, but evidently forgot about it. Anyway, as its name suggests, it’s a review by Brent Tully from a historical perspective of measurements of the Hubble Constant. I’m not sure whether it is intended for publication in a book – as it opens with the heading “Chapter 1” – but it’s well worth reading whatever its purpose. Here is the abstract:

For 100 years since galaxies were found to be flying apart from each other, astronomers have been trying to determine how fast. The expansion, characterized by the Hubble constant, H

Brent Tully, arXiv:2305.11950_{0}, is confused locally by peculiar velocities caused by gravitational interactions, so observers must obtain accurate distances at significant redshifts. Very nearby in our Galaxy, accurate distances can be determined through stellar parallaxes. There is no good method for obtaining galaxy distances that is applicable from the near domain of stellar parallaxes to the far domain free from velocity anomalies. The recourse is the distance ladder involving multiple methods with overlapping domains. Good progress is being made on this project, with satisfactory procedures and linkages identified and tested across the necessary distance range. Best values of H_{0}from the distance ladder lie in the range 73 – 75 km/s/Mpc. On the other hand, from detailed information available from the power spectrum of fluctuations in the cosmic microwave background, coupled with constraints favoring the existence of dark energy from distant supernova measurements, there is the precise prediction that H_{0}= 67.4 to 1%. If it is conclusively determined that the Hubble constant is well above 70 km/s/Mpc as indicated by distance ladder results then the current preferred LambdaCDM cosmological model based on the Standard Model of particle physics may be incomplete. There is reason for optimism that the value of the Hubble constant from distance ladder observations will be rigorously defined with 1% accuracy in the near future.

Here is the concluding paragraph:

Follow @telescoperAs the 20th century came to an end, ladder measurements of the Hubble constant were at odds with the favored cosmological model of the time of cold dark matter with Λ =0. The new favorite became the ΛCDM model with dark energy giving rise

to acceleration of space in a topologically flat universe. Yet ladder measurements, continuously improving, create doubts that this currently favorite model is complete. Yes, there is a Hubble tension.