pallidin said:
I respectfully disagree.
If we can easily notion a future infinity, why can not we see the same for the past?
The world lines come also to a "finite future end" in a black hole, so for specific world lines, there is already no "notion of future infinity". If we would have a re-collapsing universe solution, this would be the case for all worldlines, and there would not be a notion of "infinite future". In an ever expanding universe, however, yes. Then there are solutions for all t > 0 (matter of speaking).
As time is, in this paradigm, a geometrical concept, whether it is double or single sided infinite or not, is then purely a matter of the specific "shape" of the geometrical object (the specific spacetime) at hand.
Of course, it might be that the paradigm of "time is a geometrical concept" proves wrong. No scientific theory is free from the possibility of falsification (by definition, I would say!). But as long as we remain within that paradigm (that is, as long as we consider GR as a useful model for the purpose at hand), we shouldn't be surprised that "time" can have a beginning, and end, or can even loop onto itself or do other complicated things. Because time is now not "the uniformly flowing Newtonian time" as it corresponds to our intuition and daily experience.
As someone said here, a good point of comparison is "north of the north pole". People living in a non-polar region, used to limited geographical displacement (say, only walking and horse-riding), would develop the notion that "north" is a direction, something that goes on "for ever" (on a flat earth, say). For them it would be inconceivable to have such a notion as a spot on Earth where you cannot go anymore "north". It is when you understand that "north" is a geometrical concept on a sphere that you can understand that point, and not when you think of it as a "direction in a plane".
But the analogy has its limits, because the north pole is not a singularity of the geometry itself but just of a coordinate system.
I don't want to argue here about the "evidence" of having a finite time, I'm arguing here for the fact that one shouldn't be surprised to find such things in the frame of a paradigm where time is a geometrical notion.