There is no reason that it should be infinite. If matter causes spacetime curvature, which we know it does, then a universe without matter might be nearly infinite, or nearly 'flat', as even just the existence of spacetime will still cause a curvature. The more mass there is in the universe, the more it will curve and the smaller the 'observable' universe will be. So, as we have matter in the forms of gas, planets, stars etc., our universe is not infinite.
Scientists agree that the universe is expanding. This appears ab initio in the explosion of the first configuration of matter (the "Big Bang"); next, in the fact of this instability with a problematic curve that the new type of space assumes. Will the expansion accelerate? Whether spatial expansion will assume a Euclidean geometric structure at its ultimate limit, the structure of an ellipse, a parabola or a hyperbolic structure remains to be seen in its evolution. So physical space, understood always as ever-expanding referentiality to bodies in it, would appear to be finite now, but could well be tending toward infinitude as an inaccessible limit. See X. Zubiri, "Dynamic Structure of Reality," 100-101.
The acceleration of space was established ~1929 and the accelerated expansion detected in the late 1990s. There is a bit of a school of thought that this may lead to expansion into infinity and may lead to a self-destructing universe, but all these observations are not conclusive, as relative motion of our part of the universe needs to be taken into account. So, between the philosophy of Zubiri and actual measurements, and between incomplete and half-baked pictures of the universe, the introduction of dark matter, dark energy and who knows what is next, both philosophy and science is unsure. So, I gravitate towards a simple approach and apply basic principles of the General Theory of Relativity, which has to date passed all tests (those with real error bars anyway), and this leads to the understanding that the universe is not infinite, and cannot go into runaway mode. The rest... is a bit beyond me...
You can really only answer this if you first settle the question of Universe vs. Multiverse.....
Dear Marwan
In reality there are many infinities that arise in physics : the infinite discrete (e.g.. the number of stars in the universe if it is infinite) , the continuous infinity (eg. continuity of space-time) and with an infinite power superior to continuous (eg. functional integration of the measure in the file of quantum) theory)
With respect to the size of the universe , it is necessary to define a measure first , before we can classify as infinite or finite, no sense of measure, talking about "size"does not make sense . This is a complicated situation in the current context of multiverses (inclusive defining probability densities in the space of universes)
Very interesting arguments have been put forth. But still we can consider space as infinite for a very simple reason we really dont know where it ends. Once we are able to quantify space and measure the end, we can say that it is finite.
Well, Saif, my ignorance is infinite, I will admit that to you, but that does not mean that space is infinite too, right? ;)
Saif, space could very well be finite and yet have no end .... it's a common occurrence, e.g. a Möbius strip whose x axis has no end yet is finite, or the 2D surface of a sphere, finite but without an edge, and so on : lack of an edge does not necessarily mean infinite.
Reversely, the existence of an edge does not necessarily mean finite either. For instance, certain dimensions can be seen as infinite from within a black hole but finite when viewed from outside the BH .
Finally, the word 'infinite' itself is somewhat ambiguous, since there are so many different infinities. Space could be finite in some ways (such as in its 3D geographical expanse) but infinite in other ways (if spacetime is discrete, then a transfinite number - aleph naught - number of interstitial parallel universes could conceivably nestle in the cracks ...)
In other words, the question is probably a bit more complex than would seem at first blush ...
yes, for a certainty, I repeat your words, Chris: "The question is probably a bit more complex than would seem at first blush ..." Nor are the two Nelsons and other colleagues above forgotten!
Dear Prof. Marwan M. Obeidat,
I am quite late in interacting your interesting and brain storming questions.
My answer is what we know about space is naturally finite but what to be further discovered makes space still infinite.
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