Haven't seen a cosmology discussion in a bit so let's stretch our brains and consider a thought-experiment:
We've discussed the relative nature of time before - that an observer accelerating toward a distant star experiences a time differential relative to a "stationary" observer at the point of origin.
Most of us agree that the "stationary" observer (assuming he is able to observe the interior of the traveling observer's ship) views the "traveling" observer as experiencing a "slowing" of time, while the "traveling" observer (looking about his vessel and its time measuring devices) views time moving at its accustomed pace.
Where let's diverge, is to consider what happens at the opposite extreme.
Presuming that we've all made the observation that if we were to sit and observe our collective navels somewhere on the equator enjoying a "stationary" life - that our "relative" motionlessness is an illusion – we're actually rotating about the center of the Earth at an approximate one thousand mile an hour (.28 miles per second), rotating about the Sun at an approximate 18.5 miles per second and about the center of our Galaxy at an approximate 135 miles per second. And that's not counting how fast we are all rushing away from the center of our universe, which actually sounds as if it's pretty fast (and makes those first three velocities insignificant) if the cosmologists are worried that if our acceleration continues, our velocity may actually, at some point, exceed the ability of star-stuff to "hold together".
All of which is a bit of a preamble to this:
If our "traveling" observer boards his ship and accelerates away from our "stationary" observer toward the universal origin, effectively decelerating (from that tremendous velocity away from the universal origin), eventually leaving the "surface bubble" that comprises most of the observable matter of the universe, his measure of time, as observed by our "stationary" observer should begin to "speed up".
Here's the poser: What does our "no longer traveling" observer see when he finally reaches the Universal Origin, comes to Absolute Rest (at least relative to the rest of the universe), turns about and looks at our "stationary" observer? Does our "no longer traveling" observer view the "stationary" observer as a "freeze frame" image? Does our "stationary" observer view the "no longer traveling" observer vanish into infinity time? (Assuming, of course that mortality issues don't interfere).