The big rip concept comes into play when the expansion rate starts to become faster than the forces holding molecules and atoms together. As far as current cosmic expansion goes, it only applies to space between galaxies. The current expansion rate is so weak it's not enough to overcome forces that hold galaxies together.

The big rip scenario happens in the case where the rate of space expansion is increasing. It's possible, but we haven't seen any evidence of it yet, so far the rate appears constant, which means a heat death scenario.