Why does the light intensity of stars distribute almost uniformly across the night sky, if earth is not special?

Question

According to special relativity, the direction of light should change when a reference frame is moving at near-light speed. There was a question on stack exchange about this topic before: Light in Different Reference Frames. Also, I tried to plot this phenomenon: the lights uniformly emitted from one point in a static reference frame will look like this in a reference frame moving in 0.6c:

But if then, why do people on Earth observe almost uniform light intensity distributions when looking up at the sky? Why do the stars distribute almost uniformly across the sky? Does this phenomenon mean that the reference frame of the earth is special?

I suspect that this happens because the other stars, galaxies, etc. are also moving at relatively low speeds in the Earth's reference frame. Therefore, from the view of other stars, galaxies, etc., the distribution of starlights is also almost uniform across the sky, although I'm not completely confident about this explanation.

Answer 1

why do people on Earth observe almost uniform light intensity distributions when looking up at the sky? Why do the stars distribute almost uniformly across the sky? Does this phenomenon mean that the reference frame of the earth is special?

In fact, when we look closely at the cosmic microwave background radiation we see that there is a significant dipole anisotropy. This indicates that we are moving at a velocity of $370 \mathrm{\ km/s}$ with respect to the CMB "rest frame".

We don't notice this anisotropy without careful measurements because $370 \mathrm{\ km/s} \ll c$

Answer 2

The answer to your question is different for ~160 GHz microwave light and for visible light.

~160 Hz microwave light is mostly comprised of the cosmic microwave background, which (from Earth) does indeed appear significantly brighter from the direction of the Earth's "peculiar velocity" (that's the technical term) relative to the rest frame of the universe, exactly as you say.

For visible light - what we actually see in the sky with our eyes - the anistropy from the Earth's peculiar velocity is dominated by galactic-scale effects: we see many more stars from the direction of the center of our Milky Way galaxy than from other directions. There are just as many stars in every other direction, but we can't see them, because the exansion of the universe has caused (most of) their emitted light to get redshifted down below visible frequencies.

For other microwave frequencies, I'm not sure how much of the light in the vicinity of Earth comes from the CMB (or other cosmological-scale effects) and how much comes from sources within our own galaxy.