Flase wrote:I suppose there's a limit to what I need to understand, but surely for any two points in space, such as the Milky Way and the furthest galaxy to be travelling away from each other faster than light, such an infinite energy must have been applied.
Not at all. Indeed, it is possible that no energy is required (although it now appears that dark energy is responsible for increasing the expansion rate).
Paint three dots in a line on a balloon, and then blow it up. If you call the first dot your reference, the nearer dot will be moving away from that reference slower than the farther dot. Does it somehow take more energy to produce that increased speed? No. When space expands, and carries material apart, it isn't like normal, accelerated motion.
The whole Universe is expanding uniformly. The farther apart two points, the greater their relative speed of separation. So there has to be a distance where the speed between two points exceeds c. That distance is what defines the observable Universe.
It begs another question: How far away must a spaceship be from Earth before it may travel greater than c in relation to it? Even if it takes several billion years, could such a ship in theory use the slingshot effect at the galaxy centre to propel it towards a close galaxy (with redshift, say M104) and repeat the process until it is in another part of the universe travelling faster than c in relation to us?
The ship can never accelerate to c with respect to the Earth. Given enough time, it could escape from the gravitationally bound region of space created by the galaxy cluster we belong to, at which point cosmological expansion will carry it away, eventually taking it across the horizon of our observable universe- currently, about 46 billion light years away.