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In the documentary: "Curiosity - Did God Create the Universe (on YouTube)", theoretical physicist and cosmologist Stephen Hawking states that time did not exist before the big bang.
The first question that popped up in my mind was: "Could there be more universes with their own space and time?"
I will link you to some work that has been done on this idea from data from WMAP, Planck and other satellites, and the analysis therein experimentally and theoretically.
arXiv articles (highly technical):
"First Observational Tests of Eternal Inflation"
http://arxiv.org/abs/1012.1995
"Eternal inflation and its implications"
http://arxiv.org/abs/hep-th/0702178
"First Observational Tests of Eternal Inflation: Analysis Methods and WMAP 7-Year Results"
http://arxiv.org/abs/1012.3667
I'm not sure what level of inquiry would be accessible to you, but there is also a presentation with pictures that Feeney gave on a lecture tour I believe that may be more understandable if you don't have any undergraduate degree in Physics. (you may have to just skip all the math if you are unfamiliar with it).
http://www.damtp.cam.ac.uk/research/gr/workshops/PASCOS/2011/presentations/Feeney-pascos2011.pdf
In short, yet it is possible that there are "other" universes, normally formalized as manifolds endowed with a lorentzian metric. It is not a necessary condition that other universes have the same number of dimensions, or any other broad overarching properties such as the geometry of the universe. Experimentally, it turns out that our universe is very close to euclidean (meaning completely flat, a triangle inscribed in our manifold will have angles that add up to near 180 degrees). It could be that there are other universes with hyperbolic geometries, or even stranger geometries!
My personal opinion, which relies heavily on the philosophical position of ontological maximalism is that geometric topology underlies the "set of all universes" in the multiverse. I think that there is a general category of objects that can be investigated by geometric topology that describes every possible geometry that a universe can have, and that currently in the multiverse each of these objects is existing, although they may be under some type of homeomorphism. But, my personal opinion is extremely far out there, I'm fairly sure no one believes that. If you are interested in some introductory stuff on what I mentioned in the last paragraph you may want to check out this easily accessible article of geometric objects in different dimensions: http://plus.maths.org/content/richard-elwes
I think Stephen Hawking suggested that the time itself started from big bang but he never denied that there was nothing before that , he suggested that the all physical theories breaks at the very time of singularity and if there were time before that singularity , it should not effect us or our theory in any sense at all .
Rather later we know from the string theory or Model that there are possibilities of many universes which have their own physical laws and yeah space-time.I think to get the closer answer we need more time until we have clear picture with quantum mechanics and its very nature which is a puzzle by now. Until we can't combine gravity with other Grand theories , we are far from the answer.
If we begin by reducing 'universe' to 'visible universe', ie that which we can physically interact with then we can think about both: a set of bubble universes removed from us due to space-time geometry but still originating together; and the quantum mehanical multi-verse where our universe splits to accomodate those tricky qm philisophical problems.
Whether those universes have their own rules of physics is a question for some very theoretical string theory/early universe researchers.
So basically there is nothing to deny other universes but also no way we could investigate them either...
Edit: I forgot about some research in my department! There is part of the cosmology group that is looking for signatures of collisions with other bubble universes in the CMB. These could show up as ring like structures.
Some theorists interpret quantum mechanics as leading to a situation where each possible outcome leads to it's own universe.
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an actual "world" (or "universe"). It is also referred to as MWI, the relative state formulation, the Everett interpretation, the theory of the universal wavefunction, many-universes interpretation, or just many-worlds.
The simple answer to your question is that if there are other universes by virtue of the expansion we see in the universe around us, there is no way we can know anything about them directly (since the distance between them is increasing, and light can only go at light speed, so no information exchange).
Now, with that said, Velenkin thought about Alan Guth's inflation that defined the initial period of the bing-bang that vastly increased the size of the universe, and asked the question why did this inflation stop? The conclusion he came to was startling - there were other universes existing next to ours, stopping ours from further inflating! Suggesting other universes that we could know nothing about meant that Velenkin's idea was met with great hostility.
Similarly, super-string theorists trying to see mass and massless particles as strings could only make their theory work if there were many dimensions, certainly more than 3 spacial and 1 time dimensions. That raised the question why do we have 3+1 dimensions rather than the extra ones string theory suggests? The answer they came to was also startling. Several distinct universes could co-exist in proximity separated by at least 1 dimension, and such an arrangement would influence which, and how many, dimensions grew and gained dominance within a universe.
Although there is no direct evidence for multiple universes, when two or three separate, apparently unrelated theories start pointing in the same direction, it makes the circumstantial case quite appealing to physicists.
With that said, we know that space and time are related because Einstein's relativity has shown that relativistic effects affect both. For example a clock at rest will advance rapidly, as will one far away from a gravitational body. However, a clock moving rapidly relative to the speed of light will advance more slowly, almost as if that clock can either traverse time quickly or space, but not both. There is a relationship between space and time. For example, as you accelerate this same clock near the speed of light and time slows, its distance (or length) will also compress. For this reason a Cartesian view of space ceded to a more dynamic relativistic view of space after Einstein, and people began to refer to it as 'space/time'.
Therefore, if the big-bang provides evidence that all matter began to exist at some point, so did time, since space and time are related. What existed before time 0 is not a scientific question but a metaphysical one, since science typically restricts itself to what is within space/time, and studies things that are testable using observation, and repeatability (which is not to say that we cannot actually reason about metaphysical things).
