How would quarks behave in the event of 'The Big Rip'? I have always heard that you can't get a quark by itself because "the energy required to split them apart is enough to create another." But, in the case of The Big Rip, the idea is that phantom dark energy would tear molecules and atoms apart because it's a much stronger variant of dark energy. So in this case, would protons and neutrons stay together because as phantom dark energy tried to pull them apart the energy outputted would just turn back into more quarks to complete them? Or would the universe just devolve into a quark soup?
 A: In that scenario, the universe wold probably devolve into a quark-gluon plasma.
I was just reading a paper by Caldwell, Kamionkowski, and Weinberg which explores this very question. The paper is on arxiv here.
Part of the abstract reads
"Here, we explore the consequences that follow if the
dark energy is phantom energy, in which the sum of the pressure and energy density is negative.
The positive phantom-energy density becomes infinite in finite time, overcoming all other forms of
matter, such that the gravitational repulsion rapidly brings our brief epoch of cosmic structure to
a close. The phantom energy rips apart the Milky Way, solar system, Earth, and ultimately the
molecules, atoms, nuclei, and nucleons of which we are composed, before the death of the Universe
in a “Big Rip”.
A: The "big rip" is a spacetime singularity caused by "phantom energy". It is based on a classical theory (General Relativity). Whilst GR might be capable of making predictions about what happens to gravitationally bound objects, making predictions about what happens at subatomic scales to particles held together by the strong force is way outside its realm of tested applicability. In particular it takes no account of quantum mechanics.
Any answers would be just speculation at present.
