Ok.. assume that space-time is accelerating away from itself with a>0 and.. jerk - j⃗ (t)>0 (sorry - don't know how to write "a dot"! :s )..
If this continues on without the rate of acceleration ever stopping, or decreasing, the ambient temperature of the universe will fall due to its expansion in volume, approaching absolute 0 (as ours has been doing up until now). However, as the acceleration of space-time increases, at some point in time the Unruh effect would start to become significant with regards to the background temperature of the observable universe (as we assume the rate of acceleration only increases).
Would this then mean that after some time - at some extremely fast rate of acceleration - the universe would begin to "heat up" to an observer? (given jerk>0, does the background temperature of the universe plot as a convex curve with respect to time?) If so.. as the rate of acceleration keeps on increasing, could the background radiation increase enough to form a singularity?
Finally (assuming the above makes sense!), given that the observed cosmic event horizon shrinks and gets ever closer to the observer as the acceleration of space time increases, and that at some point in time the background temperature of the universe increases to a level at which singularities begin to form, if "a dot">0 still stands, the cosmic event horizon and black hole event horizon would be moving in opposite directions - one towards the observer and one away for the observer. If the two event horizons move in opposite directions, what does this mean? (I get lost here.. would this affect "a dot"?!)
(sorry if I lost you somewhere up above, if I did - could you please tell me where and why? Thank you! :D )