If you subscribe to Roger Penrose's theory, at the point of infinite expansion, the current "Aeon" will end and a new big bang will happen. As best I understand it, at the point of infinite expansion, there are only photons. Mass no longer exists therefore scale no longer exists. So an infinitely huge universe becomes indistinguishable from an infinitely small universe.

> However, after the universe finishes expanding, wouldn't it start contracting again?

Unless the answer has changed in the last several years, no, the consensus is that it's expanding too fast and has too little mass (and thus gravity) to collapse again.

(Disclaimer: not even an amateur at this, at least not for 40 years.)