While we understand the universe to have had a beginning in the big bang theory, if gravity is quantum in nature yet still has an infinite range then surely once the distance between galaxies becomes great enough, pair production will begin in between those galaxies as a result of the gravitational potential energy being converted to stable particles? This is assuming that the expansion of the universe eventually reaches a steady rate and that dark energy is infinite.

Am I missing something here? If so, what?

I propose such a fate to the universe be named the "steady-state fate" if it is worthy of serious consideration.