Hi Richard,
Choosing to call R the radius of the BB's light cone, and to identify the line BC as an upper bound on the radius of the universe were probably unfortunate over-simplifications. I tried to keep my description simple, yet accurate, and I'm afraid you found a spot where I failed to do so.
I hinted at one problem in visualizing my picture, and that is the identity of the Earth during early periods of the universe before our galaxy was even formed. It occurred to me that the stable particles (are they hadrons? I forget.)were formed early on and then during the course of the evolution of the universe, they coalesced to form galaxies, stars, planets, and us. My hinted proposal was to identify all such particles which comprise our solar system today, trace each of them back to the primordial time of interest, find their collective center of mass, and identify that point with the Earth.
That point will have a trajectory in my space-time diagram which is along the line BE. Now, using that set of points as a reference, the universe at any point along the way will have some radius.
Since the origin of the line BE is the same origin as that of all other trajectories of matter or energy resulting from the BB, it would seem to me that nothing could diverge from BE any further than BE, which is diverging and moving away from Earth's trajectory at the speed of light.
If there are events beyond that boundary, then I don't think they would be visible to us in principle, as I think you have pointed out. But my development attempts to show that even for events within the light cone of the BB, from Earth's perspective, there are events which in principle cannot be seen from Earth today, viz. those older than 9.8 billion years old.
Warm regards,
Paul |