2.4. The Horizon Feature
One can take any physical system and choose an ``initial time'' ti. The state of the system at any later time is affected both by the state at ti (the initial conditions) and by the subsequent evolution. At any finite time after ti there are causal limits on how large a scale can be affected by the subsequent evolution (limited ultimately by the speed of light, but really by the actual propagation speeds in that particularly system, which can be much slower). So there are always sufficiently large scales which have not been affected by the subsequent evolution, and on which the state of the system is simply a reflection of the initial conditions.
This same concept can equally well be applied to the SBB. However,
there is one very interesting difference: The SBB starts with an
initial singularity where a = 0 and
=
at a finite time in the past.
This is a serious enough
singularity that the equations cannot propagate the Universe through
it. In the SBB the Universe must simply start at this initial
singularity with chosen initial conditions. So while in a laboratory
situation the definition of ti might be arbitrary in
many cases,
there is an absolutely defined ti in the SBB.
As with any system, the causal ``horizon'' of the Universe grows with time. Today, the region with which we are just coming into causal contact (by observing distant points in the Universe) is one ``causal radius'' in size, which means objects we see in opposite directions are two causal radii apart and have not yet come into causal contact. One can calculate the number of causal regions that filled the currently observed Universe at other times. In the early Universe the size of a causally connected region was roughly the Jeans length, and so at the Grand Unification epoch there were around 1080 causally disconnected regions in the volume that would evolve into the part of the Universe we currently can observe. This is the ``Horizon Feature'' of the SBB, and is depicted in Fig. 2.
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Figure 2. The region of the Universe we see today was composed of many causally disconnected regions in the past. |