"Is the space inside, say, a galaxy growing but overcome by the gravitational attraction between the stars? The answer is no. Space within any gravitationally bound system is unaffected by the surrounding expansion."
View: https://youtu.be/bUHZ2k9DYHY?t=356
Sabine Hossenfelder: "The solution of general relativity that describes the expanding universe is a solution on average; it is good only on very large distances. But the solutions that describe galaxies are different - and just don't expand. It's not that galaxies expand unnoticeably, they just don't. The full solution, then, is both stitched together: Expanding space between non-expanding galaxies...It is only somewhere beyond the scales of galaxy clusters that expansion takes over."
http://backreaction.blogspot.bg/2017/08/you-dont-expand-just-because-universe.html
So cosmologists apply the expansion solutions only to voids deprived of galaxies; to galaxies and galactic clusters they apply nonexpansion solutions. Why do cosmologists resort to this trick? Because, if they applied expansion solutions to galaxies and galactic clusters, observations would immediately disprove the expansion theory. Here is why:
If expansion is actual inside galaxies and galactic clusters, the competition between expansion and gravitational attraction would distort those cosmic structures - e.g. fringes only weakly bound by gravity would succumb to expansion and fly away. And the theory, if it takes into account the intragalactic expansion, will have to predict the distortions.
But no distortions are observed - there is really no expansion inside galaxies and galactic clusters. And cosmologists, without much publicity, have simply made the theory consistent with this fact.
Since there is no expansion inside galaxies and galactic clusters, there is no expansion anywhere else. The so called cosmological (Hubble) redshift is due to the speed of light slowing down as photons travel through vacuum, in a non-expanding universe. This is not a totally unacceptable idea:
"Some physicists, however, suggest that there might be one other cosmic factor that could influence the speed of light: quantum vacuum fluctuation. This theory holds that so-called empty spaces in the Universe aren't actually empty - they're teeming with particles that are just constantly changing from existent to non-existent states. Quantum fluctuations, therefore, could slow down the speed of light."
https://www.sciencealert.com/how-much-do-we-really-know-about-the-speed-of-light