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Are there other proofs for the expansion of the universe other than red-shifting? If yes, what are those? Thank you.

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    $\begingroup$ The cosmic microwave background radiation is heavily redshifted, but its existence at all is evidence that the universe must once have been very bright and very opaque, which is only possible if the universe was once very, very dense. $\endgroup$
    – g s
    Sep 22 at 6:55
  • $\begingroup$ So do you mean that the existence of the microwave background radiation alone (without considering how red-shifted it is) is an evidence that universe was once very dense? How do we deduce universe must have been very opaque because there is the MBR? $\endgroup$
    – Xfce4
    Sep 22 at 8:15
  • $\begingroup$ The cmbr must be a snapshot of the last moment of opacity. Opacity, because it's the earliest thing we can see: it's a perfect blackbody curve, while if we were seeing other, different temperature states visible behind it, it wouldn't be. $\endgroup$
    – g s
    Sep 22 at 15:29
  • $\begingroup$ Ok, we can't see beyond it. For that reason, there is the term 'observable universe'. But leaving aside the assumption that universe is expanding (or in other words without knowing the universe is expanding already) how is cmbr a proof that the universe was very dense (therefore very small) once? $\endgroup$
    – Xfce4
    Sep 22 at 15:43
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    $\begingroup$ See physics.stackexchange.com/questions/530411/… $\endgroup$
    – ProfRob
    Sep 24 at 6:40
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A mathless, redshiftless argument for expansion:

There exists a cosmic microwave background radiation (CMBR) that fills all space.

It has the spectrum of a perfect blackbody.

enter image description here

This constitutes evidence that the entire universe was once filled with a blackbody radiator.

So far as we know, dark matter is dark, and the CMBR is light, which constitutes evidence that the blackbody radiator that filled the universe was matter.

After adjusting for gravitational lensing, the intensity distribution is almost completely uniform. The imperfections in the uniform intensity are exactly the imperfections that would be expected for a hot gas filling all space. This constitutes evidence that the matter that filled the entire universe was a hot gas.

The CMBR is visible beyond the most distant stars, therefore it is older than the oldest stars. This constitutes evidence that the hot gas that filled the entire universe was composed of nothing heavier than hydrogen.

The CMBR spectrum is a perfect blackbody. If there was another blackbody of a different temperature, or even the same temperature at a different redshift, that was older (hence - more distant) visible behind it, it would not be a perfect blackbody. This constitutes evidence that the hot hydrogen gas that filled the entire universe was opaque.

Hydrogen gas is transparent unless it is dense enough and hot enough to be a plasma. This constitutes evidence that the source of the CMBR was hydrogen plasma.

More specifically, since we can see the CMBR, this constitutes evidence that the CMBR is the last moment (in astronomical terms, thousands of years might be a moment) in which the universe was full of hydrogen plasma, after which it cooled (by adiabatic expansion) to transparent hydrogen gas.

The modern universe is nowhere near matter-dense or energy-dense enough to have a similar mass-energy density to a universe full of hydrogen plasma. Therefore the universe must be much bigger than it was when the CMBR was emitted.

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  • $\begingroup$ Thanks a lot. But without knowing that universe is expanding can we conclude that the CMBR is older than the oldest stars? I could not find the connection between being distant and old unless I assume a non-stop expansion theory. Actually it could have been like this -not very likely but just a thought-: The universe was 1/10 of its size today, there were the old stars and the former CMBR was cooled to near 0K. Then something happened, universe began to expand again and the CMBR reappeared. Some of the old stars continued and these are the ones older than the CMBR today. $\endgroup$
    – Xfce4
    Sep 22 at 23:06
  • $\begingroup$ More distant = older, full stop, unless you presuppose that the oldest stars existed forever and God swooped in and snuffed out all the more distant ones 13 billion years ago on the basis of His divine whim. More distant = older even if you suppose a collapsing, not an expanding, universe. $\endgroup$
    – g s
    Sep 22 at 23:10
  • $\begingroup$ I would suggest that "why does greater distance necessarily imply greater age" is its own, separate question. $\endgroup$
    – g s
    Sep 22 at 23:16
  • $\begingroup$ Haha. I didn't mean something like that. I was asking if distant meant older without already knowing/assuming that the universe is expanding. I might open a question on it, as you suggested. $\endgroup$
    – Xfce4
    Sep 22 at 23:16
  • $\begingroup$ "The CMBR is visible beyond the most distant stars, therefore it is older than the oldest stars. This constitutes evidence that the hot gas that filled the entire universe was composed of nothing heavier than hydrogen" this is problematic. There is no measured distance to the (source of the) CMB only one inferred from cosmological parameters. The CMB itself is of course here and now. $\endgroup$
    – ProfRob
    Sep 24 at 6:44

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