Light beam (1 photon) in the limited universe?

Question

If our universe is not infinite, what happens with the light beam (or photon) when it will travel through the whole universe? For example, observable universe according to wikipedia has diameter 93 billion light-years. What will happen with photon after 93 billion years if I generate it now? Will it return back to me? Or it will never reach the "edge" of the universe because the universe is expanding faster?

UPDATE 1

Of course, I assume that photon will no be absorbed :) because it is just a theoretical thinking. And return back I mean not exactly to the same point, but approximately within some range (let say 5% of the universe size).

Do I correctly understand that there are a few options for the case when the universe is finite (means "closed geometry"):

1. Photon will never return back because the universe will collapse before it (in case if there are no dark energy).

2. Photon will never return back because universe expanding faster than light speed.

3. Photon will come back because universe expanding slower than light. And what of these 3 options is most probable from a current scientists point of view?

Answer 1

A finite universe is said to have a "closed geometry", or to be "positively curved", meaning that, in principle, you may travel in a straight line and eventually return back to your starting point. In the 2D analogy, the surface of Earth is positively curved, and if you travel 40,000 km straight, you're back where you started.

A finite universe that does not contain dark energy of some sort, however, is bound to collapse, and you can show mathematically that even a photon will not make it back to its starting point before the universe has collapsed. Only if you consider a photon emitted exactly when the universe is created (Big Bang), it will make it back exactly when the universe ends (Big Crunch).

If the universe contains a sufficient amount of dark energy, this may prevent collapse. This may cause it to expand too fast for the photon to "get back", but you could fine-tune its components such that the expansion/collapse is slow enough for the photon to get back.

One such model is "the loitering universe", which gained some interest in the 1960's, as an explanation for an excess of quasars around redshift $z\simeq2$ (e.g. Petrosian et al. 1967). If the deceleration of matter is almost exactly balanced by the acceleration of a cosmological constant, you can have an (arbitrarily long) period of time where the universe is static.

However, observations indicate that our universe is not such a universe (Planck Collaboration et al. 2018).

Note also that since the universe is not empty, a photon may be absorbed on its way, not returning even if the expansion allows it. However, in our universe, photons that were emitted shortly after Big Bang (the so-called CMB photons) have traveled mostly freely through space ever since, with only 5% interacting with matter along its way.

Answer 2

No one can say for sure because, while we have theories which fit our observations quite well, those theories require that the universe be considerably bigger than the part we can see -- light simply not having had enough time to get to us yet. But since we don't have observations of this extended universe, we run a significant risk that we're wrong in some important way. Additionally, we know our current theories are incomplete: One of the things our theories do not tell us is whether the universe is finite or infinite. (Note: Some theories do make a prediction, but they are not supported by better evidence than theories which make different predictions. The jury -- comprised of experimentalists -- is still out.)

But we can answer your question! If the universe if infinite, the photon will never return. That's obvious. But even if it is finite, our theories show that widely-enough separated points in the universe separating faster than the speed of light due to the expansion of space, so in this case, too, the photon will never return. There is strong (but not iron-clad) evidence in favor of this picture being true.

But even if space was not expanding FTL, the photon would never come home again because space is not perfectly flat. Mass curves space and large masses (like giant galaxies and clusters of galaxies) curve space enough that we can measure it. So space acts like a very slightly ripply pane of glass, and even if it was finite and non-expanding, photons would not return home -- but they would eventually get back to within maybe ten million light-years of home as they passed by on their way around the universe a second time!

Of course this is true only if your photon doesn't get absorbed. There is a lot of stuff in the universe which absorbs photons and if a photon traveled long enough, it would eventually be absorbed.

So, say good-bye now because this is the last time you'll ever see your photon.