Can cosmological redshift be explained purely by the relativistic Doppler effect? I want to preface this by saying I don't disagree with the idea of the universe's expansion, this was just a random thought that popped into my head. I also apologise in advance if it's a duplicate, badly formatted, fairly simple or outright dumb (I'm very sleep deprived and haven't looked at the intricacies of the universe's expansion in a long time + I'm on mobile).
on to the question; how do we know that the redshift we observe while looking at faraway galaxies isn't a Doppler shift, caused by potential great attractors outside of the bounds of our observable universe? are there galaxies that have travelled "faster" away from us than galaxies that are in the same region of space, but further away from us?
if not, could this also potentially explain the differences in the perceived rate of expansion depending on what region of space you measure?
 A: "how do we know that the redshift we observe while looking at faraway galaxies isn't a Doppler shift, caused by potential great attractors outside of the bounds of our observable universe?"
The attractors you propose to be outside of the boundary of the observable universe (OU) may be approximately uniform or not. It it is uniform, than it effect on what is inside the OU is zero because the gravitational field of a uniform sphere is zero with respect to any point inside the sphere. If it is not uniform then its influence on the galaxies inside the sphere would NOT create an approximate uniform motion of the distant galaxies we see from Earth: velocity away from earth is proportional to distance from Earth.
A: Let's look at the facts.
Doppler redshift of light occurs when the distance between emitting and absorbing objects is increasing at the time of emission of light.
Galaxy clusters that were closer to us a shorter time ago must logically have been receding more slowly during inflation. The further away they were the more quickly they were receding when their light set out. The cosmological redshift we measure from nearby clusters is approximately proportional to the distance we measure (from their quasar light intensity I believe), and therefore their recession velocities at the time of emission. That's consistent with the Doppler effect.
Galaxy clusters that were further from us a longer time ago must logically have been receding more quickly during inflation. For more distant clusters as with the nearby clusters, the further away they were the more quickly they were receding when their light set out. The difference is that their light set out at a time when inflation was more rapid, so we should expect the amount of redshift per unit distance to be greater if it is due to the Doppler effect. Well that's exactly what we see.
The Doppler effect is a physical thing that's not too difficult to understand. But quite often it's the simple things that get lost amongst the more complex mathematical models.
