Frank Tipler's Omega Point
Physicist Frank Tipler envisages a similar scenario to Nick Bostrom's argument: a hypothetical cosmological scenario where, as the Universe comes to an end in a Big Crunch, the computational capacity of the Universe is capable of increasing at a sufficient rate that this computation rate is accelerating hyperbolically faster than time runs out. In principle, a simulation run on this Universe-computer can thus continue forever in its own terms, even though the external Universe lasts only a finite time.
The implication of this theory for present-day humans is that this ultimate cosmic computer will essentially be able to resurrect everyone who has ever lived, by recreating all possible quantum brain states within the master simulation.