Eebster the Great wrote:There is no pressure gradient to exploit. The negative pressure is the same everywhere. Aside from that, to do work, something needs to move. If everything is stationary, work is zero.
But the sphere is not expanding along with the rest of the space under that pressure because it's held together by the electromagnetic interactions between its atoms, so relative to the expanding space, it's as though the sphere is actually contracting, similar to what you said about the larger cosmic sphere needing to have its constituent pieces all actually flying rapidly toward each other in order to stay the same size. Except since the sphere isn't literally contracting relative to itself, only relative to the expanding space it occupies, it can go on "contracting" forever, unlike an actually contracting sphere could, at least so long as the space keeps expanding.
And as it "contracts", everything it flows past could be used to do work, which would "slow down its contraction" (i.e. make it expand), yes, if the pieces were just coasting inertially toward each other, but they're held together by electromagnetic forces, so it's the same as if you were pumping stuff into the center of a normally stationary sphere in non-expanding space: yes, it would tend to push the pieces of the sphere apart, if it weren't for something holding it together, and since there is something holding it together, that energy that would otherwise have pushed it apart can be converted into another form.
It boils down to that the parts of a non-expanding object in an expanding spacetime are moving relative to that expanding spacetime, even though they seem to be stationary in a conventional sense, and that movement is what's exploited to do work.
Consider also another analogy: you have an elastic volume filled with air, and an airtight sphere inside that volume, and then you magically teleport new molecules of air evenly dispersed throughout that volume, causing the overall volume to expand. That would cause your sphere to expand too, and the general distances between everything floating in that air; except your sphere is made of rigid, inelastic stuff that doesn't want to expand. Because of that, the pressure inside the sphere increases relative to the exterior of it, even though the same moles of air were added inside and out, in a process similar to if the moles of air had stayed constant and the sphere had contracted. Coming back out of the analogy, we're obviously not adding new molecules of anything everywhere, but there is more energy coming into being evenly everywhere, so things that remain a constant size despite that and the resultant expansion of everything else end up with an energy gradient between their interior and exteriors, as though they had contracted. An immeasureably tiny energy gradient unless you're talking about ridiculously cosmic scales, but I am talking about those scales.