Could The Big Rip Lead To Another Big Bang?

There are few questions that can keep us up at night the way pondering the eventual fate of the entire cosmos can. The stars will burn out, be replaced by new ones, which themselves will burn out, on and on until the Universe runs out of fuel. Galaxies will merge together and eject matter, while the space between bound galaxies and groups and clusters will expand forever. Dark energy causes that expansion to not only be relentless, but to accelerate. Is that necessarily the end, though? Entering speculative territory, Justin Agustino di Paola wants to know:

Could the “big rip” lead to another “Big Bang”? When the universe expands fast enough to tear atoms apart then quarks... At this point would the universe create a quark-gluon soup?

Nothing less than the fate of the Universe is at stake.