Oh there are two ideas here.
First that the universe is just very big. In that case then it may have started literally as a very tiny universe.
The other possibility is that it is now infinite. If so it was infinite during the Big bang as well.
In this case then what we know as "our universe" is just the visible part of a universe that continues infinitely beyond the horizon. And the Big Bang was due to expansion of a small part of that infinite universe.
In this case it could be that the entire infinite universe also expanded at the same time. Or could be that different parts of it behaved differently, some expanded and others didn't.
There I'm deliberately not going all the way back to the "big bang".
And just to say - I'm not speaking as an expert in general relativity. I know that in GR then they also talk about these two types of universe and the idea of a universe that starts infinite.
On physics stack exchange which is usually a good place for things like this, then you get conflicting answers, But basically the idea that it starts infinite.
How can something finite become infinite?
I think it is a bit tricky to push physics back to the big bang itself, to the very moment of the Big Bang and expect it all to make perfect sense, just as it is tricky to push physics into the extreme conditions of a black hole.
It's usually said that we have to give up on physics when it comes to singularities where you may get e.g. a million suns worth of matter contained theoretically, in a single geometrical point - and physicists are glad that they are hidden from us by an event horizon so we don't have to explain them in our physics.
I think it may be a bit like that for the origin of the universe too if you think of it as really a singularity where matter is infinitely dense and the entire visible universe becomes a point. How can a single geometrical point somehow contain all the complexity of what evolved to become our universe?
So I'm not sure what you say if you push it that far back to t = 0.
But if you are content to talk about it just a fraction of a second later, my understanding is that you have those two possibilities, an infinite universe and we see only part of it, and if the curvature is negative, that's what it has to be, if so then it is already infinite even a billionth of a second after the Big Bang.
Or it is a finite universe in which case it is possible for the whole of it to be contained in a tiny spot (though this may still be a lot larger than the part that expanded to become our visible universe). And if curvature is positive that's what it has to be.
And - when we try to measure the curvature of the universe we find it is flat, to the limits of errors in our measurements - so that doesn't decide between the two hypotheses. This is something that is actually evidence in favour of inflation which predicts that the universe would appear to us to be flat at present. It's quite hard to explain why it would be so close to flat.
According to some theories then the universe "bounced" at the origin from a previous universe that collapsed in some way, and became "almost infinitely dense" but didn't actually become a geometrical point.
And other ideas, according to conformal mapping the previous universe, when it had nothing in it left but light, lost any measure of its size and then turned into a new universe expanding from a "big bang" which may have some memories of the distribution of light in that previous vast universe.
I think there is basically lots of room for speculation and alternative theories about what happened at the moment of the Big Bang itself.
I can answer this as a mathematician. I don't know about physically possible but the idea makes sense mathematically.
E.g. start with a line segment of length 1. Double its length in the first second. Double its length in the next half second. Double its length in the next quarter second. Repeat to infinity. Then after two seconds it is infinite in length. If you think of it as a subset of the real line, then after two seconds it covers the entire line.
But I haven't seen any suggestion that the universe is infinite for this reason.
It would have to have a very rapidly accelerating expansion, like that, getting faster and faster and asymptotically an infinite rate of expansion achieved within a finite time of its origin.
Or else - it could do that instantly - at time 0 it is a single finite point. At all t > 0 it is infinite. Again you can describe that mathematically.
I haven't seen either of these though as physical suggestions. If anyone has seen any theory like this suggested, do say!
(added this after Raj Kulkarni asked me this question in the comments thread, thanks!)
First that the universe is just very big. In that case then it may have started literally as a very tiny universe.
The other possibility is that it is now infinite. If so it was infinite during the Big bang as well.
In this case then what we know as "our universe" is just the visible part of a universe that continues infinitely beyond the horizon. And the Big Bang was due to expansion of a small part of that infinite universe.
In this case it could be that the entire infinite universe also expanded at the same time. Or could be that different parts of it behaved differently, some expanded and others didn't.
There I'm deliberately not going all the way back to the "big bang".
And just to say - I'm not speaking as an expert in general relativity. I know that in GR then they also talk about these two types of universe and the idea of a universe that starts infinite.
On physics stack exchange which is usually a good place for things like this, then you get conflicting answers, But basically the idea that it starts infinite.
How can something finite become infinite?
I think it is a bit tricky to push physics back to the big bang itself, to the very moment of the Big Bang and expect it all to make perfect sense, just as it is tricky to push physics into the extreme conditions of a black hole.
It's usually said that we have to give up on physics when it comes to singularities where you may get e.g. a million suns worth of matter contained theoretically, in a single geometrical point - and physicists are glad that they are hidden from us by an event horizon so we don't have to explain them in our physics.
I think it may be a bit like that for the origin of the universe too if you think of it as really a singularity where matter is infinitely dense and the entire visible universe becomes a point. How can a single geometrical point somehow contain all the complexity of what evolved to become our universe?
So I'm not sure what you say if you push it that far back to t = 0.
But if you are content to talk about it just a fraction of a second later, my understanding is that you have those two possibilities, an infinite universe and we see only part of it, and if the curvature is negative, that's what it has to be, if so then it is already infinite even a billionth of a second after the Big Bang.
Or it is a finite universe in which case it is possible for the whole of it to be contained in a tiny spot (though this may still be a lot larger than the part that expanded to become our visible universe). And if curvature is positive that's what it has to be.
And - when we try to measure the curvature of the universe we find it is flat, to the limits of errors in our measurements - so that doesn't decide between the two hypotheses. This is something that is actually evidence in favour of inflation which predicts that the universe would appear to us to be flat at present. It's quite hard to explain why it would be so close to flat.
According to some theories then the universe "bounced" at the origin from a previous universe that collapsed in some way, and became "almost infinitely dense" but didn't actually become a geometrical point.
And other ideas, according to conformal mapping the previous universe, when it had nothing in it left but light, lost any measure of its size and then turned into a new universe expanding from a "big bang" which may have some memories of the distribution of light in that previous vast universe.
I think there is basically lots of room for speculation and alternative theories about what happened at the moment of the Big Bang itself.
COULD A FINITE UNIVERSE TURN INTO AN INFINITE ONE IN FINITE TIME?
I can answer this as a mathematician. I don't know about physically possible but the idea makes sense mathematically.
E.g. start with a line segment of length 1. Double its length in the first second. Double its length in the next half second. Double its length in the next quarter second. Repeat to infinity. Then after two seconds it is infinite in length. If you think of it as a subset of the real line, then after two seconds it covers the entire line.
But I haven't seen any suggestion that the universe is infinite for this reason.
It would have to have a very rapidly accelerating expansion, like that, getting faster and faster and asymptotically an infinite rate of expansion achieved within a finite time of its origin.
Or else - it could do that instantly - at time 0 it is a single finite point. At all t > 0 it is infinite. Again you can describe that mathematically.
I haven't seen either of these though as physical suggestions. If anyone has seen any theory like this suggested, do say!
(added this after Raj Kulkarni asked me this question in the comments thread, thanks!)
About the Author
Robert Walker
Writer of articles on Mars and Space issues - Software Developer of Tune Smithy, Bounce Metronome etc.Studied at Wolfson College, Oxford
Lives in Isle of Mull
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