In the negatively curved model the expansion of the Universe continues until its very fabric can no longer contain the expansion, resulting in what is termed the Big Rip. In a closed positively curved Universe, the Universe expands from the Big Bang singularity and then begins to collapse again into what scientists term the Big Crunch. In a flat Universe, expansion levels out and the structural fabric of the Universe continues to exist forever while its internal processes eventually succumb to heat death.
Although most scientist believe that space is flat, or almost flat, there are a few theories that favor a positively curved (or closed) structure. Among these are the finite, fundamental domain Universe that we looked at in a recent post, and the Big Bounce theory. The latter theory suggests that the Big Bang that instigated our own Universe sprang from the Big Crunch of an even older incarnation. Studies of the quantum fluctuations between each of these singularities suggest that while the physical laws of each consecutive Universe will resemble each other on a fundamental level, no two Universes will ever be precisely the same.
As I have said, the Big Bounce theory relies on our Universe being positively curved overall. I think that this theory is the most interesting of the lot, but I have arrived at some conclusions which are at odds with the standard model. For one thing I propose that our Universe actually consists of two equally sized Universes existing side-by-side. When the topology of one of these Universes is positively curved, the topology of the other is negatively curved. In this way the two Universes are always completely symmetric. At regular intervals these Universes switch their respective Universes.
They are, in effect, playing leap frog with one another.
The analogy of the leap frog game is misleading however, because it implies (as I have done) that there is more than one player. You can't play leap frog by yourself anymore than you can jump over yourself. However, in our Universal model, the two Universes are connected in such a way as to be a single Universe. The closed curvature of one Universe is merely the reversed expression of the open curvature of its neighbour. And yet the two are inextricably interrelated just like the way the concave of a spoon on one side is the natural expression of the convex on the other.
The curious thing about this theory is what happens to the seemingly separate Universes as they cross form one topology into another. In the case of a formerly closed Universe that is reaching its end in a Big Crunch, it would erupt into a massive explosion that would expand outwards into its new incarnation as a negatively curved Universe. On the flip side the negatively curved Universe would be approaching its demise in a Big Rip, partially driven by the Big Crunch on the opposite side. As both of these processes reach their culmination the topology flips and the dying Universe becomes 'reincarnated' so to speak into a positively curved closed structure.
In the violent interim between these two periods, space would appear to have a topology that includes positively, negatively and flat structured Universes all at the same time, and at different scales. It seems to me that there is enough time in this interim period, as it last almost as long as any other period on the timeline, to warrant the existence of a third incarnation of a Universe. This would mean that another big bang/crunch would have to occur as the Universes transition from the interim period into either the closed or open state.
The whole concept can be further visualized with the use of the physics of tumbling toys. When gravity acts on these toys they flip end over end. This is a lot like the way the Universe flips from positive to negative curvature and back again. For this reason I have decided to dub this theory the Tumbling Toy Universe Theory.
It could be that the Big Bounce theory is the correct one, but that its motion and topology is in fact produced by a careful adherence to the mean of both Universes proposed in Tumbling Toy. In this case all of the world lines of this Universe would cross, resulting in a massive singularity.
From a Direct Relativity perspective we could suppose that the curvature/structure of the Universe is evolving over time. To begin with, at the early stages of the Big Bang the Universe had a closed structure, this quickly evolved into the 'more-than-likely' flat Universe we see today, and will eventually develop into the hyperbolic (or negatively curved) system. This is a further example of Direct Relativity (DR) in action, see posts; Direct Relativity, Stellar Obscura, Within the Octonions. From a DR perspective this means that the Universe is accelerating (going from 0mph at the Big Bang, to light speed now, and superluminal speeds in the future) or it is rotating in some higher-dimension.
