Something has recently occurred to me which I think I should mention here. Boltzmann brains have a definite probability of "popping up" anywhere in the universe as fully formed, sentient beings. Although the odds against such a thing happening are astronomical, there is a probability which can be calculated as to their arrival. Thinking on this vein, it occurred to me that as the solar system accelerates due to universal expansion, the time relative to some stationary reality at the center of the universe would become slower for those within it. If it is the case that Earth will eventually hurtle through space at close to the speed of light, time would pass extremely slowly relative to the center mentioned previously, and the chances of weird quantum anomalies would increase. Does anyone know of calculations/work done concerning this topic? How about speculations as to the possible effects?