# A possible Test to determine if universe is infinite or not

Recently something is playing in my head over and over with the recent news about gravitational waves.

If Gravitational Waves travel at the speed of light (in vacuum). Could we not listening for a bounce back wave, as you would with waves on a swimming pool?

If the universe was confined/finite, you would be able to detect/predict a bounce back wave coming from the opposite direction, if this was the case, would detect the interference of multiple waves colliding.

This will determine if the universe is finite or not (if universe has an edge)

If time is the main issue with this kind of test (waiting time is too long)! Could we not use long extinguished supernova (which means waves have long passed us, and probably on the way back, and determine if there is an edge).

I am a little ignorant in the subject, but I thought of asking to put my mind at rest.

Would this be possible? am I onto something or am I being really silly?

In another thought, I think that the background interference could prove the universe is finite, and be in actuality the gravitational wave interference. (then again, a lot of lack of knowledge on my part on this last one).

• Mainstream cosmology does not include a universe with an "edge" as a plausible scenario. When scientists describe the universe as possibly "finite", they mean finite in the same way that the surface of a sphere is finite. The surface of the sphere is finite, but that doesn't mean it has an "edge". – Brionius Jan 17 '17 at 17:21
• This video youtube.com/watch?v=_k3_B9Eq7eM is sort of fun to watch and makes it clear why there is no edge to the universe in the sense you write about. – Lawrence B. Crowell Jan 17 '17 at 17:33
• While we don't know if the universe is finite or not, we do know that it extends far past the 'event horizon'---i.e. the region with which we can, or will ever be able to interact (technically: this is a separate inference). So that prohibits such a test. – DilithiumMatrix Jan 17 '17 at 18:59

There have been some searches for topological effects on the CMB and galaxy observations that might have occurred if our universe was not infinite, or had a non-trivially connected topology.

Topologically the universe could have flat space curvature, i.e., be what is called flat, and extend to infinity for the standard or so called trivial topology (simply connected space, a Euclidian topology $E^3$, a 3D flat slice extending forever), but it can also have other, non-trivial, topologies and be finite. Examples of k=0 flat cosmological solutions with non-trivial topologies are for instance the hypertoroidal topology (a toroid in 3D, $T^3$ which has the identical differential geometry, ie, is identical locally, to $E^3$), or the PacMan topology where what comes out of the edge of a laptop screen comes in on the opposite side (i.e., one identifies opposite edges as the same). In those cases there is no real edge, you never fall off, but some of them are finite, and open. There are a total of 17 different non-trivial topologies, some finite and some infinite. All of them are consistent with the equations of General Relativity, and the FLRW solutions.

See Cosmic Topology, from Scholarpedia

So what happens in folded topologies or the hypertorus is that light rays will be able to go travel and come back to the same place, given enough time. Of course if they are finite but very large, it might be longer than the age of the universe before they come around.

So the question is, as Dilithium Matrix pointed out, is whether we have seen some structure or galaxy or groups that seem to be repeated once or more, ie, multiple images in the observational data. The event horizon is about 16 billion lightyears out, and the particle horizon 46 billion lightyears. We've not detected any such structures, but of course we haven't minutely mapped everything out.

The article above has a section on the observational constraints and approaches to getting topological information from observational data. it relates that for finite universes, the smallest plausible models would conceivably show repeated images at about a redshift of z=2. Next decade there is a plan to map it out to z=6 or so. The CMB would also show some signs of the non-trivial topology because the causal interactions would repeat in different ways. The paper referenced describes some of the analysis done, with so far no significant signs of a non-trivial topology -- including using data from 2015 Planck.

Note also that our LambdaCDM model of the universe where the universe is pretty close to flat (Of course, we mean, always, the spatial slices) still has the .4% uncertainty around the k=0 case, so open and closed universes are still possible, and other non-trivial topologies also enter in as possibilities.

So, yes, gravitational radiation may go around, but in doing so it will loose a lot of energy. As we said, there is no real edge, but there are possible foldings where the energy may come back. It's just too far. However, the likely most significant measurements are the possible effect of those on the CMB -- the acoustic oscillations (not so much gravitational radiation but density perturbations) that caused the high and low densities seen in the CMB would have been affected by those waves going around the universe and coming back, or folding back, and some effect on the observed CMB might be seen. As noted below for the CMB, nothing significant has been observed. I do not know what the limits on the possible size of the universe from that, have not seen specific numbers on possible size limits but I don't think there have been any so far smaller than the particle horizon or it would have been widely circulated.

The other point made in the article is that non-trivial topologies have to arise from quantum effects, most probably early in the universe's evolution. It claims the General Relativity does not allow non-trivial topologies to emerge classically -- I'm not totally sure but it seems likely that it would not unless some quantum or stringy objects (e.g., large strings or branes) were involved, and then affected spacetime. Of course we don't know if black holes might not involve wormholes or other exotic geometries, and topologies.

See also the wikipedia article on the shape of the universe where topology is also discussed, as well as boundedness, finiteness and curvature. It has a few references for the data supporting the infinite flat trivial topology, but some others are not ruled out.