@Vette888,
You are conflating the Big Rip scenario with the Big Chill.
Having the accelerating expansion of the universe pull everything apart is the Big Rip scenario. It would bring the universe to an end in only 22 billion years.
In the Big Chill scenario, when the lights go out in 100 trillion (10^14) years, galaxies will retain their cohesion.
Galaxies will only lose cohesion and eject most of their mass into the intergalactic void about 10^20 years from now. The remaining mass will spiral into the central black holes by about 10^30 years.
If protons have a half life, the universe will be free of all matter by around 10^37 to 10^43 years (depending on the rate of decay). However, proton decay is only a theory and may not actually happen.