Can I use the expansion of the universe to create or destroy energy?

Question

Imagine I have a setup like this:

(The objects are not attached to each other. The red objects are much heaver than the black one, and the setup is balanced.)

This setup has a non-zero gravitiational potential energy. The red objects, if the black object was removed, would crash into each other. However, the black object is stopping this.

However, since the expansion of the universe is accelerating, there will come a point when the expansion of the universe starts to move these objects away from each other.

These objects are now moving away from each other. There are two scenarios that I think might happen:

1. They don't have gravitational potential energy anymore; they can't attract each other because of the expansion of the universe forcing them apart. As such, gravitational potential energy is now 0. However, at the time of the initial setup of these objects, the gravitational potential energy was more than zero. As such, we have destroyed energy.
2. Their gravitational potential energy increases, because they have further to fall due to the expansion of the universe. However, at the time of the initial setup of these objects, the gravitational potential energy was below what it is at the current time. As such, we have created energy.

Where is the flaw in my logic?

Answer 1

Gravitationally bound systems do not expand very much because of cosmological expansion. For example, the predicted general-relativistic effect on the radius of the earth's orbit since the time of the dinosaurs is calculated to be about as big as the diameter of an atomic nucleus; if the earth's orbit had expanded according to the cosmological scaling function a(t), the effect would have been millions of kilometers. For more on this, see this question: Can the Hubble constant be measured locally?

So yes, a local observer can detect strains and stresses due to cosmological expansion, and these are capable of doing work, but in your example, they would never be enough to achieve lift-off of the red blocks.

The fact that these forces can do work does violate conservation of energy. General relativity has local energy conservation, but no global energy conservation. See Is the total energy of the universe zero?

They don't have gravitational potential energy anymore; they can't attract each other because of the expansion of the universe forcing them apart.[...]

As a side issue, this paragraph seems to show a misunderstanding of what potential energy is. We can't define whether potential energy is zero, because it involves an arbitrary additive constant.

Answer 2

When the Universe expands, the distance between gravitationally bound objects does not increase (see here). That is why the red objects will never start to move away from each other (unless the Big Rip happens).