# Does the universe curve in on itself?

I've read a little bit about the universe, but its not clear to me if there is a place in the universe beyond which there are no stars.

For example, is there anywhere in the universe that one could go where we would not generally see stars in every direction? Its seems uncertain to me that there is.

If I were to go to the farthest star from earth magically, rather the via relatively (for argument sake). I"m guessing it would have stars surrounding it in every direction. But perhaps I'm wrong, perhaps there is some edge to the explosion of matter from the big bang, beyond which there is nothing.

Do we know if the universe curves in on itself? or is there some other dominant theory?

## 3 Answers

In the currently dominant theories, the Universe is basically the same everywhere, if you look on a large enough scale. There may not be a furthest star from Earth at all (the universe may be infinite) or it may be like "the furthest point on Earth from London" which exists, but is not a specially interesting place. The distinction between those two possibilities is exactly whether the universe "curves in on itself" (in which case it is finite) or doesn't in which case it is infinite. We don't know for sure, but any curvature is definitely pretty slight.

To see the universe as uniform, though, you do have to look on quite a large scale (billions of light years). On smaller scales than this the distribution of galaxy clusters (and so galaxies and so stars) is quite uneven, and there are places where there are no stars close enough to see with the naked eye. Nevertheless, with a big enough telescope in one of those places you would still see stars scattered in all directions.

You mention the big bang, and what you write suggests a common misconception -- that the Big Bang happened in the middle of a big empty space into which matter expands. That is not what the theory suggests. Instead all points in space, when you trace things back far enough, seem to have contained a very hot, very dense, sea of matter, which, as far back as we can extrapolate, was all spreading apart, creating new space uniformly spread throughout the old space in the process.

• Is there a formal name for the concept that the universe is curved or that it does not? – Mark Rogers Sep 3 '19 at 0:45
• @MarkRogers The only terms I've heard used are curved vs flat, finite vs infinite and bounded vs unbounded (sometimes called closed vs open). There's also a topological term called connectivity, that is, simply connected or multiply connected. Those are as far as I know, the only formal terms. The umbrella term for all of this is cosmic topology, but people often just say "shape of the universe". It means the same thing. – userLTK Sep 3 '19 at 1:31

We don't know.

The answer to this question hinges on whether the universe is open, flat, or closed. These are technical terms arising from the Friedmann equations. The math is not trivial, but the gist is there is a so-called critical density:

$$\rho_c = \frac{3H^2}{8\pi G}$$

If the average density of the universe is above this value, then the universe is closed. You can still travel forever without reaching an edge, not dissimilar to how you can travel forever on the Earth and not fall off. If it is equal to this value then the universe is flat, and if it's smaller than this value, it's open. In the latter case, the universe has negative curvature, like the middle part of a saddle. In both these cases, the universe is infinite.

It turns out that the observed density of the universe just happens to be about $$\rho \approx \rho_c$$.$$^1$$ This is a mystery that is a major motivation for the theory of Cosmic Inflation.

1. If it were exactly $$\rho_c$$, that would also be a major surprise because there's no reason to expect an exact result like this. More accurate is to say that the current constraints on $$\rho_c$$ are very close to $$\rho_c=1$$. I don't know the exact numbers off the top of my head, but last I saw they looked something like $$\rho = 0.998^{+0.004}_{-0.007}$$ (please do not take this number to be precise; it's only meant as an illustration). Therefore, all three universes are still possible.

Over a sufficiently long period, anything repeats. So it could be said that the universe curves on itself. Currently, Cyclical cosmologies are in vogue. These describe the universe as reaching a minimal information point and therefore reaching their original state. Although Cosmic Inflation cannot be directly observed, if you were to travel to the end of the universe you would end up where you started in these cosmologies.