> “The memory is nothing but the change in the gravitational potential,” said Thorne, “but it’s a relativistic gravitational potential.” The energy of a passing gravitational wave creates a change in the gravitational potential; that change in potential distorts space-time, even after the wave has passed.
Conservation of energy gets a bit screwy with these kinds of cosmic models. Partially because there isn't a single direction of 'time', but also because all kinds of energy gets stored in the fabric of space-time which can cancel out all kinds of things.
Not to mention that there's no reason to assume conservation of energy still holds if the laws of physics simply change over time (which would be the case in the simplest possible theory were all interaction distances simply shrink over time).
> “The memory is nothing but the change in the gravitational potential,” said Thorne, “but it’s a relativistic gravitational potential.” The energy of a passing gravitational wave creates a change in the gravitational potential; that change in potential distorts space-time, even after the wave has passed.
Gravitational waves are that energy.