First, I should admit that we are having a dark, rainy autumn here in Sweden, so this post might be a bit more doom and gloom than my usual cheerful "let's think positive about grey goo" posts :-)
I read the Krauss and Starkman paper "Life, The Universe, and Nothing:
Life and Death in an Ever-Expanding Universe" (astro-ph/9902189) and
it is really bad news. Their basic argument is that the positive
cosmological constant that seems likely given current data will lead
to accelerating expansion, and this will in turn make the de Sitter
horizon creep inwards. The de Sitter horizon for an observer is the
horizon from which no new information can reach the observer - a
signal sent from beyond it will race towards the observer at the speed
of light, but due to the expansion of the universe the distance will
steadily increase and the signal will never reach its
destination. Currently it seems to be 18 billion lightyears away
(given the estimates of density and the constant today), but in just
150 billion years everything outside our local supercluster will have been redshifted by a factor 5000.
This is bad news for astronomers and us who want to see all of the universe, but the long term effects are even worse. In the really long run the amount of mass-energy that can be gathered and used for information processing will be limited. Krauss and Starkman does an analysis of how much can be extracted within the de Sitter horizon. If the universe is matter-dominated then the amount of matter that can be collected is finite if the density perturbation spectrum is too smooth, and if it contains enough large-scale density perturbations it is hard to avoid gravitational collapse into a black hole (however, I'm much more sanguine about this possibility than the authors). If the universe is radiation-dominated things are much worse, since to get an infinite amount of radiation you need a much larger mass than is containind within the visible universe. Superstrings doesn't work as energy sources either.
Worse, in cosmological constant dominated universes Gibbons-Hawking radiation exists that provides a background temperature which puts a limit to the efficiency of computation, which rules out Dysons hibernation trick to survive for an infinite length of time on a finite amount of energy. Also, they point out that quantum fluctuations will make any finite alarm clock fail eventually, which is of course bad, and that systems become thermally uncoupled from each other which makes cooling ever harder.
They suggest that we could survive for 10^50-10^100 years, but that is after all just a small part of eternity.
So it seems that Tipler (expanding universe rather than big crunch) and Dyson (infinite survival in open universe) are out. Fortunately we have a third candidate for transcendence, Linde. What if we can escape to other regions of the universe or make baby universes?
"Eternal inflation, black holes and the future of civilizations" by
J. Garriga, V.F. Mukhanov, K.D. Olum and A. Vilenkin
The simplest possibility would be to leave messages in "bottles" and
wait for the inflaton field to tunnel to the top of the potential;
this happens with a very low probability for positive cosmological
constants. The "bottles" would then be found by civilizations in the
new universes or build a descendant civilization. Unfortunately the
probability of black holes emerging from quantum fluctuations is much
higher, so one has to send an absurd number of bottles to be
reasonably sure - around exp(10^122) or so.
(astro-ph/9909143) is much more upbeat. It is aware of the previous
paper and looks into how life can survive. It also assumes that indefinite survival in one of the inflation bubbles will not be possible, but that it might be possible to send information to later civilizations (or send a probe to make them) so that one's civilization can go on indefinitely.
The simplest possibility would be to leave messages in "bottles" and wait for the inflaton field to tunnel to the top of the potential; this happens with a very low probability for positive cosmological constants. The "bottles" would then be found by civilizations in the new universes or build a descendant civilization. Unfortunately the probability of black holes emerging from quantum fluctuations is much higher, so one has to send an absurd number of bottles to be reasonably sure - around exp(10^122) or so.
Making baby universes seems to be a better idea. Collapse matter into a black hole, and hope the high densities causes inflation and the emergence of a baby universe region inside. Unfortunately the probability of nucleation seems to be rather low (i.e. extremely low, exp(-10^14)) if one has a big black hole, and for small black holes the information that can be sent through them is limited by Bekenstein's bound. They get estimates of information on the order of 10^13-10^68 bits, which isn't that much (OK, I'm an xerophile who want to lug around an arbitrary amount of papers).
Fortunately, if the weak energy condition can be overthrown, then negative energy densities can be used to make inflation easier, and larger black holes can be used which enables more information transfer. They point out "Since the future of civilization depends on the outcome, this can be regarded as a good reason to increse funding for negative energy research!" :-)
Overall, the outlook is rather gloomy, but (you knew I couldn't possibly end on a low note) there are some hopeful possibilities. One could imagine using the matter collection scenario of Krauss and Starkmann to make a number of huge black holes in which to escape into new inflation regions using negative energy densities. Some of these will likely have better values of the cosmological constant or at least ones closer to zero - this way one could construct a Dyson-Linde scenario, with possible offshoots into the Tipler scenario if descendant civilizations happen to find themselves in closed universes.
Perhaps the most optimistic thing about these two papers is not their conclusions, but the fact that physical eschatology and the effects intelligent life can have on the universe are not being increasingly studied by physicists. It is hardly a mainstream topic, but it is no longer utterly beyond the pale.
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! firstname.lastname@example.org http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y