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I am trying to reconcile two facts:

  1. That galaxies' comoving velocities are generally close to zero, and

  2. That the universe has no preferred reference frame.

Galaxies seem to move very little relative to each other, aside from motion due to the expanding universe. This is why astronomers can use redshift as a measure of distance. However, this suggests that there's a preferred reference frame -- the one we're in! In every other reference frame, galaxies must have a non-zero comoving velocity on average.

It seems like there are a few possible resolutions to this:

  1. The universe DOES have a preferred reference frame, and we currently occupy it. In any other reference frame, galaxies would all have a significant peculiar velocity in the same direction. For example, if we launched a ship at 0.5c right now, observers on the ship would see a blueshifted universe in front of them and a redshifted one behind them, and could conclude that they were in a moving reference frame.

  2. To an observer traveling near c relative to us, the universe looks exactly the same: The galaxies they see ALSO have very little comoving velocity. In this case, the relativistic observer sees the same thing we see and there is no preferred reference frame

  3. There is a preferred reference frame, but only locally -- where "locally" means in the observable universe only. Over the entire universe, galaxies have a wide distribution of peculiar velocities. However, before inflation occurred, small regions of matter already "agreed" on a shared reference frame. Then, after inflation, the entire local universe became one of those regions with a preferred reference frame.

I feel like the third explanation is the most likely. Is this the right conclusion?

(Context: I'm currently taking my first grad-level cosmology course, and this question has been itching at the back of my mind for a few weeks.)

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In general relativity a reference frame need not be inertial.

The universe does have a preferred reference frame. It is the one in which the CMB radiation is isotropic to first approximation. This is also the frame in which velocities of galaxies relative to the frame are zero on average. In cosmology it is called the "co-moving frame" and observers at rest in this frame are called "fundamental observers". Such observers find the CMB to be isotropic, and at any given cosmic time they also all agree on its temperature. But these observers are in motion relative to one another in the following sense: the length of a rod stretched between any pair of them changes with cosmic time. (The 'rod' here being millions of lightyears long so not a practical thing, just a thought-experiment). So your point 2 is correct if the two observers you have in mind are far-apart fundamental observers.

None of the above breaks the principle of relativity, because for the purpose of mathematical analysis one can always adopt other frames if one wishes, and the Einstein field equation will still have the same mathematical form.

Finally, all this has nothing to do with any early period of cosmic inflation, because even if there had not been any such early period (and the evidence is ambiguous) then the above would still be true.

The smooth nature of the cosmic expansion gives an example of the fact that the early conditions of the universe were very special, and this remains a puzzle. Inflation does not solve this puzzle because it too requires special initial conditions.

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  • $\begingroup$ @safesphere Thanks for option 2 point which I have clarified. Regarding puzzle, I agree the horizon problem is ill-stated and therefore not a genuine physics problem, but I think it remains the case that physics has little or no purchase on the question of initial conditions of the cosmic expansion. If one tries to estimate whether the conditions could be regarded as drawn at random from a state space, then most estimates (admittedly rather back-of-the-envelope) suggest the answer is a resounding no. $\endgroup$ – Andrew Steane Oct 18 '19 at 16:47

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