In the context of CTE, the event that precipitated the Big Bang, was more of a tiny spark than a large explosion. The special nature of this spark was that it was one of curvature, and that its magnitude was enough to overcome the intrinsic resistance to curvature inherent in the proto Universe that preceded it.
With this in mind, the original proto Universe can be described as a one dimensional Universe whose dimension is space-time and whose value is curvature. The nominal value of the curvature is zero, but it may fluctuate randomly. As long as the magnitude of the curvature never gets above a specific threshold, this Universe will be stable. This threshold is the amount of curvature it takes to curve the Universe in on itself. The intrinsic resistance to curvature allows the Universe to bend and not break in the presence of small curvature perturbations. The resistance is a consequence of the strength of reaction being limited, which is what ultimately results in the speed of light being limited. If the intrinsic resistance was zero, curvature perturbations could not occur. An analogy would be that the perturbations dampen out immediately if the resistance is zero, but dampen out over time when the resistance is finite. This is not exactly correct since time really doesn't exist yet. In this case, the dampening is over space-time.
As long as this 1-dimensional proto Universe is stable, that is, at time zero, time can be considered as randomly fluctuating around zero with an average value of zero. The limiting threshold of curvature then corresponds to a specific time as well, and when exceeded, initiates the arrow of time. In this proto Universe, it's easier to conceptualize the relationship between curvature and its space-time dimension as a measure of the relative phase difference between time and space.
As long as the magnitude of the curvature alternatives between positive and negative values such that its space-time average value is less than the critical value, the Universe will be stable. When the limiting amount of curvature occurs, time gets so far ahead of space that space can not keep up and a new spatial dimension arises in order to reconcile this gap. Note how the timelessness of the 1-dimensional proto Universe means that in the presense of random curvature fluctuations, the limiting amount of curvature is destined to eventually occur. In this new Universe, the value at any point is also curvature, but here, curvature is a little more complex, although, it still maintains the intrinsic property of being a measure of the phase difference between time and space.
The intrinsic resistance to curvature is still a fundamental part of this new 2-dimensional Curvature Universe. As a consequence, at the instant time separates from space, an amount of negative curvature (anticurvature) is created to offset this initial spark. These 2 curvature components, the initial positive spark and the reactionary trailing negative component, appear in this new Universe as 2 independent entities, owing to their separation in time, and are soon thereafter, doubled into 4 and then 8 and then 16 with each generation doubling the total amount of curvature and anticurvature present in the new Universe. The splitting of space-time into separate spatial and time dimensions prevents the reactionary opposite curvature from exactly cancelling out the original curvature as it was able to do in the 1-dimensional Universe that preceded.
As the content of the Curvature Universe exponentially increases, it will oscillate between ever increasing values of curvature and anticurvature until it either curves in on itself or uncurves away from itself. When a Universe curves in on itself, a new dimension is created. An analogy for this is that when a one dimensional line is sufficiently curved such that its ends meet, it becomes a two dimensional circle. Similarly, when a Universe uncurves away from itself, a dimension would be lost. When a Universe curves in on itself, it is always the space-time dimension that splits off another spatial dimension and the progenitor dimension retains its core characteristic of being space-time. Even the time dimension of the current Universe is really space-time owing to the finite speed of light. The finite strength of action combined with a separation, albeit not complete, of space and time also implies that a Universe which curves in on itself does not just snuff itself out, but instead, transitions to a new state with an additional degree of freedom. This results in an increase in Entropy by distributing the original energy across an extra dimension and is similar in concept to an expanding gas. This would seem to imply that from a thermodynamic point of view, such a state transition is irreversible and that a Universe uncurving away from itself can not actually happen unless energy is added to the system. Two possibilities for a reversing process would be proton decay or the decay of Black Holes, but neither of these are certain at this time.
Based on Entropy arguments and by what the Universe looks like today, we can say that the Universe curved in on itself and in the process, the space-time dimension split again, resulting in a new 3-dimensional 'Energy' Universe. The two resulting spatial dimensions of this Universe are more closely related to electric and magnetic fields than they are to spatial dimensions as we know them now, although the space-time dimension is fundamentally unchanged.
This exponential expansion continues until the Energy Universe folds in on itself creating yet another dimension. The result is the 3 spatial dimensions and the space-time dimension of the current 'Matter' Universe. After this last stage of the evolution, the exponential expansion stopped.
To understand why the expansion stopped, consider the SOE's. In the 2-dimensional Curvature Universe, SOE's were discrete points along a line. In the 3-dimensional Energy Universe, the SOE's were circles corresponding to the dots in the preceding Universe. In both cases, the curvature and anticurvature were indistinguishable owing to the separation of time and space. In the final 4-dimensional Matter Universe, the SOE's formed spheres. At this instant, all of the anticurvature was on the inside and the curvature was on the outside. Locally, they were able to exactly cancel each other out and a new state of stability was reached.
Space, as we perceive it, did not exist until the final split. This is consistent with Inflation theory, but offers a more reasonable explanation for the mechanism behind it. The time over which the evolution occurred needs only to span 275 or so generations before enough curvature is created to account for the Universe as we can observe it today. The whole process took only a tiny fraction of a second.
At the end of this expansion, the Universe was comprised of galactic size balls of primordial gas separated by galactic scale distances. These balls of gas were cold and dark, but gravity quickly collapsed them into massive star like objects which became Quasars and ultimately the super massive black holes at the center of all galaxies. The rest of the matter comprising current day galaxies was material ejected far enough away from the active Quasar as not to be consumed by the black hole that would eventually result.
An interesting consequence of this quick collapse was that the resulting curvature took on a bimodal distribution. It had a large peak at the center where the black hole evolved and a smaller peak, representing the history of the original distribution, at a distance away from the center. These two peaks end up attracted to each other, forming a stable potential well of curvature within which, the stars of the galaxy eventually formed. We observe this curvature distribution today and attribute it to Dark Matter. However, Dark Matter is not an exotic form of matter, but simply part of the curvature function representing the central black hole of the galaxy and a consequence of its rapid formation.
The single zero curvature point in the original proto Universe evolved into the Universe we see today. Each circle of SOE resulting from the expansion after the first dimensional split eventually became a galaxy and each sphere resulting from the final split became a particle. Because of the initial random fluctuations of curvature, the resulting sizes of the galaxies are not all the same, nor are they evenly distributed. The initial distribution would be something along the projection of the lines connecting the dots resulting from the first dimensional split, which over the eons, the combination of gravity and the advance of time would evolve into something like the galactic distribution we see today.
There are three conclusive echos of this process which we can observe today. The first is the CBR, which is an echo of the random curvature perturbations that precipitated the formation of the Universe. It's non zero average value is a reflection of the critical space-time separation that kicked off the process. The second echo is the frequency of charge, or the Compton frequency, which is an echo of the rate of expansion. The nature and magnitude of the curvature asymmetry associated with charge is also a reflection of the initial critical condition. The third echo is the photon, which is a translation of the circular SOE's of the Energy Universe into the spiral SOE's of the photons we observe today.
There are also a few more speculative echos of this process. One is the neutrino, which has a circular SOE and is a more direct echo of the Energy Universe than the photon. Another possible echo is the fine structure constant which appears to be exactly right for the number of generations of expansion that occurred between the 3-dimensional Energy Universe and the current 4-dimensional Matter Universe and the split that preceded. If this number of generations happened twice, the number of equivalent particles that exist would be 4**137 which is consistent with the apparent number of particles that exist in the Universe. The fine structure constant appears to be more closely related to the intrinsic resistance of the Universe to curvature and a connection to the number of generations has not been established yet.
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