You humans think of time in an odd way.
you think of it like a line.. but what is a line?
by your definitions, anything which continues indefinitely in both directions.
But to those ends, time is hardly a line at all.. it HAS a beginning.
So perhaps its more like a ray. An object with a start but no end.
But time doesn't elapse when there is no difference in velocities between objects.. so it has an end, too.
So perhaps its a line segment. A beginning and end..
But maybe, just maybe, it doesn't end at all.
Perhaps the death of one universe leads to the birth of another..
Since time is reliant on the difference in velocity between objects, any identical universe to the current one would loop the time "line"
The idea is that any system which decays into another alters the second simply by the status of the first upon death. 1 > 2 > 3 > 1 > 2..