Epistemic Status: Mix of facts, far-future-speculation with the inevitable biases from only considering techniques we know are physically possible, fermi calculations, and an actual spacecraft design made during a one-week research bender.

(this is a sequence. 2, 3, 4, 5)

Part 1a: Gotta Go Fast, Astronomy is a-Wasting

Once a civilization or agent grows up enough to set it sights on colonizing realms beyond its host planet as its first priority (instead of averting existential risks), there is a very strong convergent instrumental goal which kicks in. Namely, going as close to lightspeed (abbreviated as c) as possible.

This is because the universe is expanding, so there is a finite sphere of reachable galaxies, and more pass outside the horizon every year. IIRC (60% probability), about half of the galaxies in the Hubble Ultra-Deep Field are unreachable even if we traveled at lightspeed.

Arriving at a galaxy even one year faster nets you a marginal gain of (one galaxy of stars)*(average stellar luminosity)*(1 year) of energy, which for our Milky way comes out to about $1.6 \times 10^{44}$ Joules. Assuming energy production on earth stays constant, that's enough energy for a billion years of earth civilization, 130 trillion times over. And I'd expect a transhuman civilization to be quite a few orders of magnitude better at getting value from a joule of energy than our current civilization. And that's just for a single galaxy. There are a lot of galaxies, a one-year speedup in reaching them has tremendous value.

This is basically Bostrom's astronomical waste argument, except Bostrom's version then goes on to apply this loss in total form (which is far larger) instead of marginal form, to argue for the value of reducing existential risk.

Now, there are a few corrections to this to take into account. The first and most important is that, by the Landauer limit, the amount of (irreversible) computations that can be done is inversely proportional to temperature, so waiting until the universe cools down from its current 2.7 K temperature nets you several orders of magnitude more computational power from a given unit of energy than spending it now. Also, if you do reversible computation, this limit doesn't apply except to bit erasures, which nets you a whole lot more orders of magnitude of computation.

Another correction is that if there are aliens, they'll be rushing to colonize the univ...