If there were expansion, it would be in competitive interaction with the gravitational attraction and the effects would be manifest wherever there is such an attraction. For instance, the expansion would dominate where the attraction is weak, and vice versa. No such effects have ever been observed. Cosmologists don't know how to model the local interaction between expansion and gravitational attraction (any such model would produce results incompatible with observations) and implicitly obey the following idiotic slogan:

Wherever there is gravitational attraction, forget about expansion!

The problem (for cosmologists) is that recently Sabine Hossenfelder made the implicit slogan explicit:

Sabine Hossenfelder: "If The Universe Is Expanding, Then Why Aren't We? 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." https://www.forbes.com/sites/startsw...ding-universe/

The universe cannot be expanding in some places and static in others - it is static everywhere. Star light slows down as it travels through the space vacuum, an effect caused by a factor equivalent to vacuum friction. For not so distant stars this is expressed as Hubble redshift but beyond a certain distance the star light does not reach us at all (Olbers' paradox):

"This leads to the prediction of vacuum friction: The quantum vacuum can act in a manner reminiscent of a viscous fluid." http://philpapers.org/rec/DAVQVN

"...explains Liberati. "If spacetime is a kind of fluid, then we must also take into account its viscosity and other dissipative effects, which had never been considered in detail". Liberati and Maccione catalogued these effects and showed that viscosity tends to rapidly dissipate photons and other particles along their path, "And yet we can see photons travelling from astrophysical objects located millions of light years away!" he continues. "If spacetime is a fluid, then according to our calculations it must necessarily be a superfluid. This means that its viscosity value is extremely low, close to zero"." https://phys.org/news/2014-04-liquid...uperfluid.html

Natu "As waves travel through a medium, they lose energy over time. This dampening effect would also happen to photons traveling through spacetime, the researchers found." http://www.nature.com/news/superflui...hysics-1.15437

"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-muc...s&limitstart=1

Vacuum friction slows down photons coming from distant stars - so the Hubble redshift is produced - but at the end of their journey photons redshift less vigorously than at the beginning. This has wrongly been interpreted as accelerating expansion:

"In the mid 1990s two teams of scientists, one led by Brian Schmidt and Adam Riess, and the other by Saul Perlmutter, independently measured distances to Type 1a supernovae in the distant universe, finding that they appeared to be further way than they should be if the universe's rate of expansion was constant. The observations led to the hypothesis that some kind of dark energy anti-gravitational force has caused the expansion of the universe to accelerate over the past six billion years." https://cosmosmagazine.com/physics/d...-may-not-exist

The redshifting occurs in a STATIC, not expanding, universe, and varies EXPONENTIALLY with time. The "finding that they appeared to be further way than they should be" is an illusion due to using an approximation to the exponential function.

Assume that, as the photon travels through space (in a STATIC universe), a factor equivalent to vacuum friction (see relevant references below) slows it down so that the photon loses speed in much the same way that a golf ball loses speed due to the resistance of the air. On this hypothesis the resistive force (Fr) is proportional to the speed of the photon (V):

Fr = - KV

That is, the speed of light decreases with time in accordance with the equation:

dV/dt = - K'V

Clearly, at the end of a very long journey of photons (coming from a very distant object), the contribution to the redshift is much smaller than the contribution at the beginning of the journey. Light coming from nearer objects is less subject to this effect, that is, the increase of the redshift with distance is closer to LINEAR for short distances. For distant light sources we have:

f' = f(exp(-kt))

where f is the initial and f' the measured (redshifted) frequency. For short distances the following approximations can be made:

f' = f(exp(-kt)) ~ f(1-kt) ~ f - kd/λ

where d is the distance between the light source and the observer and λ is the wavelength.

The approximate equation, f' = f - kd/λ, is only valid for short distances and corresponds to the Hubble law.

The original equation, f' = f(exp(-kt)), shows that at the end of a very long journey (in a STATIC universe) photons redshift much less vigorously than at the beginning of the journey. This means that photons coming from very distant objects have undergone some initial "vigorous" redshifting which is unaccounted for by the Hubble law. This explains why the very distant objects "appeared to be further way than they should be if the universe's rate of expansion was constant".

Pentcho Valev