The primary reason models of the future break down pass the singularity is due to the creation of super human intelligence. In theory it is impossible to predict the level of technological progress by minds superior to our own. With this said one such problem that will most like be left up to Artificial intelligence to crack would be that of interstellar travel and time travel.
Of-course any such developments in faster than light travel would also be accompanied with an advancement in our understand of the universe and the physics that govern it. I expect our understanding of the universe and our place in it to drastically expand into a more holistic universal view.
Already theoretical physics is toying with ideas that our entire universe is but a fraction of what exist in a multidimensional space, or a bubble within a greater fabric of possible realities/universes. So with the idea that something exist beyond the fabric of our own reality, science will seek to puncture or open a gateway into other dimensions/realities/ universes, a task that may be taken over by our creations. This scientific wizardry is not of artificial ingenuity, but rather a current fantastical concept by our human theoreticians, so one can only imagine what lies beyond the minds ability to grasp.