In my layman understanding current prevailing theory is that acceleration of expansion will reduce observable universe, and as consequence there is basically no question of "size beyond observable universe" - there is no possible interaction with it and as such it doesn't exist.
> In my layman understanding current prevailing theory is that acceleration of expansion will reduce observable universe, and as consequence there is basically no question of "size beyond observable universe" ...
Yes, but that was true before the Dark Energy discovery. It's predicted to become much worse in the far distant future because of the acceleration caused by Dark Energy, and eventually there will be comparatively small island universes -- galactic clusters -- that will remain gravitationally bound far into the future, after the remainder of the universe has receded from view. This is because galactic clusters are below the threshold for being affected (i.e. torn apart) by Dark Energy.
> there is no possible interaction with it and as such it doesn't exist.
Yes to the first, no to the second. At present, we cannot see beyond a certain time horizon, but cosmological curvature measurements take this invisible mass-energy into account even though it's not directly observable. Our present conjecture that the universe is infinite in size (based on curvature measurements) obviously implies a universe most of which isn't visible, but all of which affects the measurements.
Most physicists[1] would dispute the conclusion that "as such it doesn't exist." They would simply say that there can be no interaction with anything beyond the horizon---that stuff out there is certainly... out there.
http://en.wikipedia.org/wiki/Accelerating_universe