That is not dead which can eternal lie: the aestivation hypothesis for resolving Fermi's paradox
Anders Sandberg, Stuart Armstrong, Milan M. Cirkovic
If a civilization wants to maximize computation it appears rational to aestivate until the far future in order to exploit the low temperature environment: this can produce a 1030 multiplier of achievable computation. We hence suggest the "aestivation hypothesis": the reason we are not observing manifestations of alien civilizations is that they are currently (mostly) inactive, patiently waiting for future cosmic eras. This paper analyzes the assumptions going into the hypothesis and how physical law and observational evidence constrain the motivations of aliens compatible with the hypothesis.
As far as I can tell, the paper's physics is correct (most of the energy comes not from burning stars but from the universe's mass).
However, the conclusions are likely wrong, because it's rational for "sleeping" civilizations to still want to round up stars that might be ejected from galaxies, collect cosmic dust, and so on.
The paper is still worth publishing, though, because there may other, more plausible ideas in the vicinity of this one. And it describes how future civilization may choose to use their energy.
I'm surprised at the lack of any 'when the stars are right' quips. But anyway, this has the same problems that jcannell's 'cold slow computers' and most Fermi solutions:
More to the point, anything that DOES use matter and energy would rapidly dominate over things that do not and be selected for. Replicators spread until they can't and evolve towards rapid rates of growth and use of resources (compromising between the two), not things orthagonal to doubling time like computational efficiency.