[yk]

Conservation of energy may or may not be valid in general relativity, at least in a naive understanding of conservation of energy. The technical explanation for this is, that conserved quantities are related to geometrical symmetries via Noethers theorem [1], and on a curved background these symmetries may or may not be there. ( A rather handwaving explanation would be, that there is no straightforward way to define the energy density of a gravitational field.)

In fact it is possible to build a perpetuum mobile by just filling some region of space with dark energy. This region of space will then expand at constant energy density, therefore creating energy.

[1] https://en.wikipedia.org/wiki/Noether%27s_theorem

[maxerickson]

"In fact it is possible" is a pretty strong way to talk about moving something that might not exist.

[yk]

Agreed, the wording is rather strong. But at least it is shorter than: "According to current understanding of GR and the contents of the universe it should be possible."