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In the recent $100m search for extra terrestrial life project project, Stephen Hawking is quoted in the following way:

"We believe that life arose spontaneously on Earth," Hawking said at Monday's news conference, "So in an infinite universe, there must be other occurrences of life."

My understanding is that scientists believe that the universe isn't infinite - there there is a finite number of stars, it's continuously expanding but has a finite size at a given time.

What's Stephen Hawking refering to here?

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Due to the finite speed of light, and the finite age of the Universe, only a portion of it is observable. When people talk about "the size of the Universe", "the number of stars in the Universe", etc., they usually refer to the observable Universe, i.e. the sphere in which we are centered, and which has a radius given by the distance light has been able to travel in the 13.8 billion years since the Big Bang. Note that since the Universe is expanding, this radius is more than 13.8 billion light-years. In fact it's 46.3 billion light-years.

Observations indicate that, on large scales (i.e. above roughly half a billion light-years), the Universe is homogeneous (the same everywhere) and isotropic (the same in all directions). Assuming that this is indeed true is known as the cosmological principle. If the rest of the Universe follows this principle, then there are three possible overall "versions" of universes that we can live in. We call these versions "flat", "closed", and "open". Whereas a globally closed universe would have a finite extent, globally flat or open universes must be infinitely large.

The observable Universe is, within measuring uncertainties but too a very high precision, flat (e.g. Planck Collaboration et al. 2016). Hence, we might think that the whole Universe is, in fact, infinite. But sort of like standing in a large forest with limited visibility doesn't tell you whether the forest is just larger than you can see, or if it's infinitely large, we can't with our current theories and observations know whether the Universe is finite or infinite.

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    $\begingroup$ Well, no. All the observations indicate is that the chunk we see is flat and homogeneous. There is no possible observation that could positively conclude that the universe is infinite, for obvious reasons. There's always the question of what may be far beyond the current limits of observation. $\endgroup$
    – Florin Andrei
    Commented Jul 26, 2015 at 18:51
  • $\begingroup$ Yes, you're right, of course. I do like to think that the rest of the Universe is similar to what we see, though. $\Omega_\mathrm{tot}$ is so close to unity, and in the past is has been tremendously more close to unity. But you're right, the only thing we can say with some certainty is that the Universe is much larger than what we can see. $\endgroup$
    – pela
    Commented Jul 26, 2015 at 19:14
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I believe his meaning is being misinterpreted as a claim that the universe actually is infinite. If someone says "in an infinite universe", they are not asserting that the universe is indeed infinite (as no scientist could ever claim to know), they are simply saying "if the universe is infinite." It is merely a case from which to begin the discussion. For example, if you were having a discussion about whether to pass a seatbelt law, you might start with "in a world where people always make the safer choice in everything they do, we would not need seatbelt laws." That would not be a claim we live in such a world, it is merely setting a kind of baseline for going on to talk about what is the actual situation.

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A relativistic universe which is expanding faster than light (like ours) is effectively infinite for all practical purposes.

Also due to its relativistic nature and faster than light expansion, even if you assume it's not infinite at some given moment, it still doesn't have any edges or borders - for you. You're in some random place in it, the maximum speed of any possible interaction is speed of light, and the universe is expanding faster than light - then anything that happens at some (real or imaginary) "edge" is outside your realm of existence. It is effectively infinite - for you.

Give it enough time and it would grow as big as you want. Give it asymptotically infinite time and it will grow asymptotically infinite.

As to what the "edge" might be, see Eternal Inflation. This is a model in modern cosmology where local bubbles like ours have stopped inflating (they still expand, but not at the tremendous rate of the initial inflationary phase); however, inflation continues forever outside the bubbles and at the edges. Therefore the bubbles keep growing indefinitely at faster than light speeds. Because speed of light is a limit for any interaction inside the bubbles, for any internal observer each bubble is effectively infinite for any practical purpose.

Be aware that there is no proof that this is actually the case, but this is a model that fits well what we now observe.

EDIT: TBH, I'm not even sure this is a question for StackExchange. It's very open-ended, and we don't really have the conclusive answers. All we can say for now is that the universe appears to be infinite for all practical purposes, but we can't know for sure. So often scientists like Hawking just simplify the language and refer to the universe as "infinite" without any of the qualifiers that would be required in a strict context.

I don't think there's any single, final answer here.

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  • $\begingroup$ But isn't the fundamental assumption behind Hawking's statement that there is an infinite number of planets? How does "effectively infinite" address that? $\endgroup$
    – Pete Becker
    Commented Jul 26, 2015 at 19:23
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    $\begingroup$ It doesn't. There's a fundamental difference between "absurdly humongous beyond imagination" and "infinite". But I think most astronomer/physicists think that the Universe is in fact infinite, lest it would conflict with the cosmological principle, which we wouldn't like. $\endgroup$
    – pela
    Commented Jul 26, 2015 at 19:39
  • $\begingroup$ Also, +1, but note that the term "expanding faster than the speed of light" necessitates a a chosen distance scale, since expansion rate is proportional to distance. The part of the Universe that is closer to us than roughly $10^{10}$ lightyears recede at speeds lower than that of light. $\endgroup$
    – pela
    Commented Jul 26, 2015 at 19:43
  • $\begingroup$ @PeteBecker In a relativistic universe (like ours), there is an upper limit to the speed of any interaction. Nothing can reach arbitrarily far away, arbitrarily quickly. That being the case, there is no practical difference between an universe infinite-right-now, and an universe which is expanding faster than light over very large scales. In the Eternal Inflation model, the bubble doesn't even have an edge - the "edge" is the place/time where/when the universe is young, perpetually created, eternally inflating. An observer there would simply see a younger universe, that's the only difference. $\endgroup$
    – Florin Andrei
    Commented Jul 26, 2015 at 22:05

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