The Sky in 350 Billion Years

The universe is much larger than the observable part  -> we are surrounded by a much more massive part of the universe... which in itself is expanding with some inertia... wouldn't that 'pull' our observable part there off apart*, adding to the observable expansion rate and look an awful lot like dark energy? do current models of expansion factor that in? because i know, back in the naughtys, when I did amateur astronomy, the idea of a universe bigger than the observable part, was not yet well understood, but theories and debate of crunch vs. heat death already progressed quite a while.

* like a  tidal pull, distributed perfectly homogeneous around the observable part, under the common assumption, that the universe overall has homogenous mass distribution.
on second thought: that tidal pull would dilute over time, but also grow in volume at a the rate of the speed of light. what would it mean, under the assumption the universe turns out to be infinite? does it pull itself apart, generating energy, by sheer geometric relation, at the volumetric growth rate, to exactly _not_ break energy conversation, just by keeping the ratio between energy, that shouldn't exist and space, that just recently didn't exist yet constant?