An infinite number of universes is a very different concept from an infinite universe. The two can not exist together, you have one or the other. An infinite universe assumes a universe that goes on for ever and ever, after the big bang it will just keep on expanding. If it keeps on expanding it means there can be no parallel universes as the universe will expand into their space.
Therefore at first glance it seems nonsensical to talk of an infinite universe and an infinite number of universes. Therefore all the universes in a multi-verse world must have a limit. This of course can be easily refuted by suggesting that though boundaries/ limits of the universes can be touching they do not need to touch on all sides thus leaving one side open for continual expansion. One can illustrate this in their mind by taking boxes and lay them side to side, say an infinite number of boxes. One can then put infinite number of boxes on top and at the bottom and at the back but leaving the fronts with no boxes. This means a single box has other boxes on 5 sides. and all have no boxes on the same side leaving room for infinite expansion on that one side. This would make sense in combining the idea of an infinite universe, infinitely expanding as well as a multi-verse existence.
However, though novel the thought pattern above is it destroys the notions of dimensions. Higher dimensions bind in lower dimensions. Therefore any concept of an infinitely expanding universe might very well contradict the idea that higher dimensions exist. What higher dimensions essentially supports is that there are an infinite number of universes at every dimension until we reach an infinite dimension. There is only one universe of infinite dimensions that can exist. All other dimensions exist inside the one infinite dimensions, this is still a massive universe and we probably do not understand more than 0.1% of it.
If dimensions exist, and they have to, logic, the very fact that 2 + 2 = 4 at times when dealing with knowledge and 2 + 2 = 2 at times, (the basics of the principles of transdimensional mathematics, we can call this the khumalo principle as I was first to bring this concept and show it is always correct) heavily lean towards the concept of dimensions, in fact are best proof of existence of dimensions thus far.
However when people misunderstand dimensions they confuse themselves. They confuse themselves as to satisfy their intellectual curiosity to ignore one of the principle laws of knowledge, the law of consistency. This is the case with the so called brane theorem proposed by Paul Steinhardt and Neil Turok. They suggest that other 3 dimensional reality could be right next to us suspended in higher dimensions. This is not understanding dimensions, it is breaking mathematical concepts understood in high school. It would be laughable if it was not because of how the media supports them they are taken seriously. It is advantageous to be born of the elite, politics everywhere including science. This thought comes from biblical stories that angels just appeared from nowhere, Steinhardt and Turok are just attempting to make it into physical reality. What they are simply implying without knowing it is that at higher dimensions there is an overlap of dimensional planes, illogical.
Why overlapping. Think about it, if there is another 3 dimensional universe suspended in hyper-dimension, meaning suspended in a higher dimension, then there is an overlap off dimensions at that higher level. Then with the laws of consistency then with all the technology, we can see 13.7 billion light years the edges of our universe, why have we not seen overlapping in the third dimension, why is our universe not overlapping with another. Turok and Steinhardt where not ready to put forward such a theory, did not fully understand dimensions. We are not talking of the world of the dead, or spirit world, we are talking of the living.
An infinite number of one dimensions make a 2 dimensional plane. An infinite number of 2 dimensions make up a 3 dimensional plane. An infinite number of 3 dimensions make up a 4 dimensional plane. It then becomes nonsensical to suggest that there is a 3 dimensional universe right next to us suspended in higher dimensions. Build up from basics, do not throw basics away when trying to fix a problem you do not understand. Any universe that overlaps ours is a universe of higher dimensions strictly because though our existence is confined to 3 dimensions, right now we exist in a 4 dimensional universe that is wrapped up by a 5 dimensional universe that is ultimately wrapped up in an infinite dimensional universe.
As we exist right now influences of higher dimensions are everywhere because a 3 dimensional universe exists in these higher dimensions. The greatest influence however is the 3 dimensional universe we exist in, but all other dimensions have influence. There is no suspended universe of 3 dimensions, that is breaking consistency. The next three dimensional universe is at the boundary of our 3 dimensional universe.
Basically what this article is saying is that our universe ultimately has to be limited if there are higher dimensions. Reason and logic are more and more pointing towards higher dimensions. Therefore this universe has to have a boundary to allow the existence of higher dimensions. The universe is only unbounded at infinite dimensions, but nothing ever changes at infinite dimensions, it is timeless. Either higher dimensions exist or they do not, that is the question of boundaries on the universe.
Dimensions by mathematical logic must limit our universe, but greatly expand existence.
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