We know that the light we measure from distant galaxies is red-shifted; the red-shift is proportional to distance; we attribute this to the expansion of space at the rate of the Hubble constant/parameter over time.
Hypothetically, if space was not expanding, would the wavelength of emitted light be constant for all distances away from the source?
What experiments have been performed to test this?
Update
After doing some more research, my question is related to the nature of the "redshift-distance relationship". Clearly, this relationship exists because we can measure it using standard candles etc. Expanding space is the generally accepted explanation, of course; however, there are alternate theories such as, Tired Light, one of which suggests light changes wavelength over distance via some yet unknown mechanism, and Chronometric cosmology where redshift is a side effect of permeating 3-sphere space.
My question can then be rephrased:
Is the redshift of light from galaxies 100% correlated to the expansion of space, or is there the possibility that other factors and mechanisms also influencing the redshift of light en-route from a distant source to us?
E.g. Is it possible that the wavelength of light can change as it permeates through space, in addition to the effects of the expansion of space?
What experiments have been performed to confirm one way or the other?
I ask because I have never heard of such experiments. If no experiments have been performed to test this, it suggests it is only an assumption that the redshift of light from galaxies is 100% correlated to the expansion of space.
One experiment that comes to mind would be to measure the apparent 'tightness' of galaxy clusters by redshift. The apparent 'tightness' of galaxy clusters should be different based on expanding space, vs tired light.
The Tolman surface brightness test is referenced as a reason to discount "tired light", but from what I understand of the test, it oddly assumes a constant wavelength and energy for the tired light scenario, and therefore it doesn't discount a tired light mechanism.
According to this wiki article there were 6 tests "that were conceived in the 1930s to check the viability of and compare new cosmological models". Unfortunately, there is no mention of what the other tests are. It would be nice to know.
