[set fair (OP)]

I was thinking about very distant galaxies which seem to be too developped for their age. If the universe is finite and unbounded, then we might be seeing galaxies which we coud see closer to us of we pointed our telescopes in the opposite direction. I realise that this thought must have occured to other people but I can't find an answer by Googling. So I'm asking here.

[Kryptid]

Yes, I've heard this before myself. If I recall correctly, there have been searches for such "doubling" of galaxies (the light traveling around the universe in one direction to get to us and then around the other direction as well, giving the illusion of two galaxies where there is only one). I don't think anything definitive has been found.

[paul cotter]

A galaxy or cluster of galaxies might look very different from a different viewpoint. As such it could be very difficult to identify two images to be from one source.

[evan_au]

If the universe were finite and shrinking (one of the possible solutions of Einstein's equations), the light from distant galaxies would show galaxies at more distant places than they are "today" (bearing in mind that "simultaneous" does not really exist in Einstein's equations). This would allow an answer of "YES" to: "Could the universe be smaller than the visible universe?"

However, Hubble's observations (both Hubble the man, and the space telescope named after him) show that distant galaxies are red shifted, and moving away from us, which is different solution to Einstein's equations.
That means that the light we see from distant galaxies would show galaxies closer than they are "today"

The Nobel-winning discovery of Dark Energy in the 1990s show that the expansion is accelerating (another solution to Einstein's equations).

So according to this latest information, the answer is "NO" to: "Could the universe be smaller than the visible universe?"

[evan_au]

PS: We still don't know if the universe is finite or infinite.

If the universe is infinite, the concept of a "smaller size" is meaningless (or at least, ill-defined).

[paul cotter]

I could be very wrong here(most likely!) but I thought that Einstein's equations gave two solutions, one an expanding and one a contracting universe and he had to add the cosmological constant to allow a static case. I don't think there was a case of expansion speeding up.

[evan_au]

Einstein's equations gave two solutions

A brief history of modern cosmology: Around 1915, Einstein produced a field equation describing the cosmos. The calculation generated an (unknown) constant of integration (as integration always does).
- Einstein's original paper omitted mention of this constant. It was mentioned in a later version.
- As usual in mathematics, you try to find some known condition that allows you to identify the value of this integration constant
- Einstein followed the cosmological assumption of his day that the universe was eternal and unchanging, and this "known condition" allowed him to define a value for this constant.
- Around 1925, Belgian priest Georges Lemaitre (perhaps with a Bible-inspired cosmology) saw in these equations the possibility of what we now call a "Big Bang"  creation of the universe. Same equation, different range of values for the cosmological constant, and different initial conditions.
- In 1929, astronomer Edwin Hubble saw that the universe was expanding. This confirmed Lemaitre's suggestion. At this point, the cosmological constant was assumed to be zero. Same equation, different value for the cosmological constant.
- In the 1970s, Vera Rubin saw that galaxies rotated in a strange way, and this led to the idea of Dark Matter. Same equation, same value for the cosmological constant, but introducing the concept that the mass of the universe is a combination of "normal" matter, and the dominant "Dark" matter.
- In the 1990s, the accelerating expansion of the universe was discovered, attributed to Dark Energy. Same equation, different value for the cosmological constant.

Einstein's field equation has proved remarkably resilient for over a century.
- New theoretical, computational and experimental techniques for investigating it have repeatedly confirmed it to an incredible accuracy
- With applications including black holes, GPS, gravitational waves, gravitational lensing and frame dragging
- Discoveries in this time have changed the interpretation of various parameters in the equation, but the equation itself has stood the test of time.
- Some very recent satellite measurements of the expansion of the universe have called into question just how constant this "cosmological constant" truly is. We will need more data to confirm if it has changed, and if so, in what manner
- An engineering "law": "All constants are variable" (under different conditions)

https://en.wikipedia.org/wiki/Einstein_field_equations#The_cosmological_constant