An O'Neill cylinder for those not in the know is basically a space habitat consisting of a rotating cylinder 32km long and 8km in diameter. I want to turn one into an actual spacecraft rather than a habitat. Assuming the ones building/retrofitting this enormous spaceship are god-like posthumans, what are some potentially theoretical energy sources I could use to explain how they get something this massive moving so quickly in a relatively short period of time?
For ships of this mass, the only sensible means for propulsion are off board power being beamed to the ship.
Scaling a laser driven sail in the manner of Robert L Forward's proposal is a bit of a stretch at this scale, the small exploratory spacecraft he proposed required massive sails, a focusing lens over a thousand kilometres in diameter and a battery of solar power stations and lasers in orbit around Mercury with a beam power measured in Terawatts. Scaling this up is simply a matter of engineering. A post in NextBigFuture about Tabby's star speculated the variable light curve was caused by large mirrors orbiting the star, with some the size of the Moon's orbit around the Earth.
With a mirror of that size reflecting sunlight, the author had the following to say about the system:
How massive would a similar size ‘solar sail’ mirror be? Well, unlike Dyson spheres, mirrors, and especially sails can be quite thin, so figuring on some tens of grams per square meter one gets ~2e16 kg, something like the mass of an asteroid with diameter of order 20 km would suffice as building material.
The light pressure in the ‘beam’ from the initial mirror would supply twice that pressure to this lightsail upon being reflected, sufficient to provide the sail a constant acceleration of several times g=10m/s^2. By hanging a starship of similar mass on the sail, the acceleration can be made equal to that of the passenger’s home planet, and all the inhabitants of the planet could indeed probably be accommodated in a ship of such mass simultaneously. At 1 g constant acceleration they could journey ‘anywhere’ experiencing only a couple of decades of onboard time due to time dilation (or less than one decade at 2 g’s).
Stopping at the destination can be done using a smaller ‘drouge shoot’ mirror-sail deployed out the back of the starship. Meanwhile, he original sail in front would be released, but the reflected annular beam from it would strike the deceleration sail and the starship slows. This would require an optically controlled original sail.
While not trivial, this is simply an extension of existing technology, and with a continuing program of building and development, larger and larger structures cold be built to accommodate larger and larger starships.
The primary difficulty is you are essentially creating a Nichol-Dyson beam, and could destroy entire planets that get caught in the beam. You would either need to aim out of the plane of the ecliptic, or find a way to shutter the beam as planets came into range.
How about an Alcubierre drive? If your god-like posthumans are able to manipulate negative matter in some way, they'd be able to create a warp bubble around the cylinder and get it moving, not just at fractions of c, but multiples of c.
If you really do want to stay below c, try a kugelblitz drive - a small black hole, created by focusing a lot of laser energy into a small enough point. You can then use the hawking radiation of the black hole to drive your ship.