# Is the universe finite or infinite?

I thought the universe was finite, but then I read this:

How can something finite become infinite?

And they seem to assume it is infinite. So which is it?

It's impossible to know whether the universe if finite or infinite because we'll never be able to see it all. Note that genneth says "and for simplicity the universe is infinite", and this is the key point really. It makes Physics simpler if the universe is infinite so we tend to assume it is.

But you need to consider what you mean by "infinite". It doesn't make sense to say the universe has an edge, because you then have to ask what happens if you go up to the edge then take one more step. That means the only alternative to the universe being infinite is that it loops back on itself like a sphere, so you can walk forever without reaching an edge, but eventually you'll be back where you started.

We don't think the universe is like a sphere because for that spacetime would have to have positive curvature, and experiments to date show space is flat (to within experimental error). However spacetime could be positively curved but with such small curvature that we can't detect it. Alternatively spacetime could be flat but have a complex global topology like a torus. The scale of anything like this would have to be larger than the observable univrse otherwise we'd have seen signs of it.

Incidentally, if the universe is infinite now it has always been infinite, even at the Big Bang. This is why you'll often hear it said that the Big Bang wasn't a point, it was something that happened everywhere.

Later:

I've just realised that you also asked the question about time beginning at the Big Bang. In the answer to that question I explained how you use the metric to calculate a geodesic, with the result that you can't calculate back in time earlier than the Big Bang. You can also use the metric to calculate a line in space at a fixed value of time (a space-like geodesic). Our universe appears to be well described by the FLRW metric with $\Omega$ = 1 that I mentioned in the other question, and if you use this metric to calculate your line you find it goes on forever i.e. the universe is infinite.

But then no-one knows for sure if the FLRW metric with $\Omega$ = 1 is the right one to describe our universe. It's certainly the simplest.

• a manifold can be topologically closed and have zero intrinsic curvature. a n-cube with their opposite sides identified become a n-torus. It would still seem locally to be flat – lurscher Apr 19 '12 at 15:46
• I said in my answer that the universe could be a torus! – John Rennie Apr 19 '12 at 16:24
• ah well, it seems i'm sorely missing some glasses – lurscher Apr 19 '12 at 16:53
• Is it so unreasonable to have a universe with an edge? Quantum mechanically, the probability of moving past an infinite square well goes smoothly to zero at the boundary (eg. extra dimensions orbifolded on $S^1$) – James Apr 19 '12 at 19:57
• An edge would presumably be somewhere that a geodesic stops. In this sense the universe has an edge at the Big Bang, and there are also edges at black hole singularities. Apart from these, I can't see how you would define an edge for the whole universe. – John Rennie Apr 20 '12 at 9:58

The current, widely accepted model for cosmology is $\lambda$-CDM. The universe appears (exactly) flat, and for simplicity the universe is infinite. Note that we distinguish between the observable universe (which is the local patch that light could have travelled between since the Big Bang) and the totality — we have constraints that even if the universe is not infinite, its size is many orders of magnitude larger than the observable one.

In the literature (especially the popular science one) the details are very muddled, because the consensus around $\lambda$-CDM model is quite recent — relying heavily on detailed measurements of the cosmological microwave background radiation, largely done by WMAP in the last 8 years or so. In a sense, the lay reader should be exceedingly careful when she reads statements (even from heavy-weight scientists) regarding cosmology — it is (perhaps ironically) a fast moving field.

• I have a problem here: isn't the "observable" universe lacking a definite definition? You can point the CMB, but that's wrong. There was interaction before the genesis of CMB radiation, it just happens to be the case that before the CMB the universe was opaque so we can see that. But that interaction should still be considered in an entropic accounting of the universe. The observable universe could be infinite, but the information is irrevocably obscured among the sea of subsequent particle interactions. The formation of our galaxy could have been affected by something now 1000 bly away. – Alan Rominger Apr 19 '12 at 16:04
• @AlanSE: see en.wikipedia.org/wiki/Observable_universe for details. The definition is quite specific, and precise. Note that I was slightly misleading in my parenthetical remark, since the real definition is based around causal influence, rather than actual photons. – genneth Apr 19 '12 at 16:30
• Oh ok, the intent of your answer does make sense. I have trouble grappling with the claim that the observable universe is only about 2% larger than the visible universe. That would seem to have major direct implications on the answer to this question. I don't think it's trivial as to whether or not we have a finite or infinite past-looking light cone of interaction, but the claim would seem to be that astronomical observation has shown it to be finite. It would also just seem odd to me for a finite universe to have spatial dimensions $\gg$ the time dimension. – Alan Rominger Apr 19 '12 at 17:44
• @AlanRominger The time dimension has also other different features from the spatial ones. – peterh - Reinstate Monica Oct 5 '16 at 16:51
• "the lay reader should be exceedingly careful when she reads statements (even from heavy-weight scientists) regarding cosmology — it is (perhaps ironically) a fast moving field." I do not see why a layman should be careful just because the field is moving fast. By now I guess about anyone understood that what one knows is never static (those how didn't have anyway sever problems). – Rudi_Birnbaum Mar 14 '18 at 20:44

There is always the problem when answering this question that General Relativity, naively interpreted, allows you to speak about the part of the universe which is not observable from our vantage point, and this makes the question nontrivial.

But in a logical positivist perspective, the one suggest strongly by string-theoretic holography, the universe is exactly the stuff inside the cosmological horizon, and it is finite because the cosmological horizon is of finite area. There is no objective meaning to stuff outside the cosmological horizon, so there is no point in thinking about this--- it is meaningless in the sense of Carnap.

• If the universe is "mathematically" finite, it could be, that we see duplicates of galaxies (see en.wikipedia.org/wiki/Observable_universe). – jjcale Dec 5 '12 at 20:20
• @jjcale: I am pointing out that regardless of identifications (which are not experimentally found), the obervable universe is finite, so one must be a positivist and take this seriously, and not do unpositivistic speculations about a hypothetical exterior. – Ron Maimon Jan 4 '13 at 3:18

Nobody knows. But most probable theory says it is infinite.

UPDATE

The general theoretical description of Universe is given by Friedmann–Lemaître–Robertson–Walker metric. This metric allows Universe to be both finite (closed) and infinite (opened). This depends on k parameter. If k<=0 then the Universe is infinite. Current observations show that k is close to zero, which can mean either infinite or very big (much larger than 14 billions of ly which is observable space size).

I treat this as it is most probably infinite.

UPDATE 2

Lambda-CDM model cannot itself answer the question if the Universe is finite or not. This is just a summation of observable data about what Universe is consist of.

• Maybe you could elaborate on this theory in your answer? – Manishearth Dec 6 '12 at 10:33

Although the general theoretical description of the Universe is given by Friedmann–Lemaître–Robertson–Walker metric, and although it allows the Universe to be both finite (closed) and infinite (opened), scientific observation has shown that the universe began a finite period ago (approximately 13.798 Billion years ago). There was a big-bang, inflation of the universe. All motion of stars and nebula are travelling away from each other from an apparent singularity, and this 'bang' left residual heat and still evident structure (to the universe).

Along the 'time axis' in the negative direction then, the universe is finite. Along the time axis in the positive direction it may be theoretically possible for the universe to age infinitely, but it has't yet, and at every point aging in that direction the universe will still be finite back to its origin. At no point in the future will the age of the universe be infinite, and it isn't currently.

So the age of the universe is currently and will only ever be finite. (Besides, David Hilbert proved that it is physically impossible to have an infinite change of events, so even as we approach infinity, the universe's age will be finite, perhaps very large, but still finite).

The universe cannot be infinite because everything has a limit and infinity is not apllied to stuff which is real

• would you mind to justify your answer? – c.p. Jan 30 '13 at 23:56
• "everything has a limit" [citation needed] – ACuriousMind Nov 10 '14 at 19:36