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Thought experiment that prompted the question. Imagine two masses existing in orbit in the far future nearing a big rip so that inflation should be noticeable. It would seem that space expanding should exert a force on them that would change their orbit resulting in them moving farther apart. This would seem to require energy input. Further imagine rockets applied to the masses to slow them down so the masses fell into each other. The longer you let inflation work on the distance between the masses before they're unorbited, the farther they fall. The higher the fall the more gravitational acceleration, the more kinetic energy. This would seem to indicate the mass's potential energy increases as inflation happens.

Is it correct to conclude from that thought experiment, that inflation creates energy? Is the thought experiment flawed?

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Inflation does not quite work that way. The objects are not pinned to a point in space, so as space expands, they just move to maintain their relative potential energy.

That being said, in Lagrangian mechanics, we do see that inflation introduces a time-dependent term which means energy is no longer a conserved quantity. But the process is more subtle than, say, inflating a balloon and watching points drift apart.

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  • $\begingroup$ Thanks for your answer! I didn't think about the fact gravity would be acting on the two masses during inflation to preserve their relative positions $\endgroup$
    – netsplit
    Jul 1, 2022 at 16:34
  • $\begingroup$ But I read that if inflation is fast enough, it will even rip atoms apart, so two masses do not necessarily remain at the same distance. How that agrees with what you just answer? And if they move to keep their relative potential energy, would not that make their kinetic energies increase? So total energy goes up? $\endgroup$
    – user338734
    Jul 1, 2022 at 16:41
  • $\begingroup$ @CarlosGauss There is an effect, its just more subtle than the obvious approach to thinking about inflation. It doesn't just add kinetic or potential energy to objects in the simple way. We typically model such things using Lagrangian mechanics with a time varying Lagrangian, and then find the stationary path as usual. You do see an increase in total energy, but it's just not the obvious increase you might expect. $\endgroup$
    – Cort Ammon
    Jul 1, 2022 at 16:47
  • $\begingroup$ Thanks!........ $\endgroup$
    – user338734
    Jul 1, 2022 at 16:55

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