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If energy is "not conserved" in General Relativity (or at least, it is difficult to define it) in the context of an expanding accelerating spacetime (like it happens in our Universe), are there any observations of deviations from the strict conservation laws in the evolution and formation of large scale structures (like clusters or superclusters of galaxies for instance)?

vengaq
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  • Energy is only conserved in systems with time translation symmetry. The universe is, whether we like it or not, not time-translation symmetric. On the plus side... the question where the energy for the creation of the universe came from is also easily answered by this fact: energy is not conserved, hence the universe can create as much of it as it likes. – FlatterMann Oct 26 '22 at 19:05
  • @FlatterMann the thing is that we don't have any observed and proved evidence that shows that the universe is creating energy anywhere (you can say that dark energy is increasing but as dark enerry is still hypothetical, it does not count as proved evidence, which is what I'm looking for) – vengaq Oct 26 '22 at 20:25
  • The point is that in a scenario where energy is not conserved it is pointless to look for a source of energy. It's not there because it is not necessary. The entire conservation law accounting scheme only works in scenarios with the necessary symmetry. The universe as a whole does not have it. – FlatterMann Oct 26 '22 at 20:34

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Perhaps someone will add in a more interesting answer later on, but I'd say cosmological redshift is an example. You have a beam of light losing energy to the Universe's expansion, and hence turning more red. I've done some calculations exemplifying how this means non-conservation of energy in this post, but for simplicity I worked with a closed universe that recollapses, as it allows a somewhat more natural definition of energy.

Níckolas Alves
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  • thanks. I was thinking more in something like the trajectories of the galaxies (or the clusters) or maybe their formations, not light itself. Anyways, I'm interested in finding any example where the conservation of energy is "broken" at cosmological scales and the system "gains" energy (instead of "losing" it). The closest thing I can find is that since the density of dark energy does not decrease as the universe expands, its total amount increases. However, as dark energy is still somewhat hypothetical, I was looking for other examples with other "conventional" types of energy @NickolasAlves – vengaq Oct 26 '22 at 16:20