Infinity simply means "endless, forever, unbounded"... . Since "space" demonstrably, had a beginning and is expanding at a measurably ever incresing velocity, it does not fulfill the definiton of "infinite"...
The universe does not have a boundry, it is the boundry.
When we look out deeper and deeper into space in all directions we find we are surrounded by its beginnings ~14 billion years ago, and so it would appear from any point "within", due to the extreme yet limited velocity of light. The ultimate end, where ever that may be lies in the future where it remains to be seen. In the mean time this moment is the end . . . for now. That's what I think.
If the whole is the universe that does not answer a question about parallel universes (if they ever existed). Analogies have been made with our universe about a balloon that is expanding. Our conception therefore is that space exists outside the balloon.
The shape of the universe has been a matter of intense research pretty much from the begining of time.
Up to about 10 years ago the answer you'd have got was that it was too close to call.
General relativity tells us that matter bends space and the amount of matter we knew was there was so close to the amount needed to make space bend back on itself that we were really unsure whether it was open or closed.
Then there's the matter of the multi-verse there are certain fundamental constants which seem fine tuned to give us a universe where matter exists, stars shine and life can evolve. This has lead people to ask whether we are in fact in one of billions of subtly different universes. This rather calls into question even something as simple as what we mean by "Universe".
In short the discoveries of the last 10 years or so have thrown a lot of irons back into the fire and until we have a proper understanding of dark energy and dark matter we're unlikely to have a good answer for what it is - although we can be pretty certain that it didn't start with apple trees and talking snakes
What do I mean by opened or closed? Well I'm sure you remember the game asteroids. In that your little spacecraft would go off of the screen on the left and reappear on the right. This is a closed universe in 2D.
You can visualise this as the surface of a Torus (a bagel or ring doughnut). It's not a sphere because if you travel off of the top you come back to the start without visiting the same place that you visit if you go off of the left and reappear on the right (think about it).
(sorry about that the copy and paste seem to have messed things about a bit)
So a closed Universe might well be like that a 4 dimentional hyper-bagel.
But times change and most notably we discoverred dark energy. A force that means that contrary to what we understand the inflation of the universe is accelerating. Today few people would tell you that the Universe is closed. It does however have an event horizon. The acceleration of the universe and it's initial inflationary peroid means that there are places vanishing over the invisible boundary where you could not reach even if you travelled forever at the speed of light.
It's a bit like being trapped in a gigantic black hole. .
If you accept that an atom resembles the solar system.
It has a nucleus, ( The sun ) And Neutrons & Protons
( The planets ).
What if these are universes in micro-miniature ?
It would make " splitting the atom " Genocide on a massive scale.
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Sorry, I had to type this as they will not allow pens, pencils or sharp objects in here.