Does the energy density of the universe decrease when objects become gravitationally bound?

Question

We know that the mass of an Iron nucleus is proportionally lower than the mass of a hydrogen nucleus (a proton) compared to the sum of the individual nucleons. This is due to the binding energy of the nucleus, and would I be right in thinking that this binding very much does decrease the energy density of matter in the universe, while increasing that of radiation (the radiation emitted during nuclear fusion?
My question is that when stars and galaxies become gravitationally bound to each other, the energy of the system also decreases and hence the total energy density of the system must decrease too - there by decreasing the energy density of the universe. Where does this energy go? And is the average energy density in galaxies and clusters appreciably lower than it would otherwise be due to this tight binding of matter?

CookieNinja · Accepted Answer

No. When hydrogen became iron the energy "loss" didn't disappear it became radiation. Locally the energy decreased but globally the energy remained in our universe and resulted in 0 change to the total. Same is true for galaxies, they shrink by shedding mass, radiation and energy through gravity waves (think that covers all?). The energy doesn't disappear, it just leaves the local system leaving the global sum unchanged.
The only thing I think would alter the energy density of the universe is its expansion. The volume increases but the energy sum remains the same so density should decrease. But please don't quote me on it, I may have overlooked something.

Does the energy density of the universe decrease when objects become gravitationally bound?

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