There was no Big Bang. There will be no Big Crunch.
Everything recycles through blackholes and is re-emitted into the Universe as via Hawking radiation/evaporation. "Virtual" pairs produce real particles, which produce real atoms, and the whole process starts over again.
Space/Time isn't just curved, it's completely bent. Trying to map it with any of our current technologies is like trying to map the Amazon with an Etch-a-sketch.