I Deviations of conservation laws in cosmological evolution?

[Suekdccia]

TL;DR Summary

Deviations of conservation laws in the context of cosmological evolution?

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)?

For example, in some articles about the study of galaxies and clusters evolutions and formations, sometimes the effects of the "tidal force" from spacetime expansion is considered... Has the expansion changed the energy or momentum of these systems somehow?

 

[PeterDonis]

If energy is "not conserved" in General Relativity

This doesn't mean what it seems to mean.

When you think of "energy conservation", you're probably thinking of local energy conservation: roughly speaking, that energy can't be created or destroyed in any local process. That is still true in GR; its mathematical expression is that the covariant divergence of the stress-energy tensor is zero.

What "energy is not conserved" in GR actually means is that, except for certain special cases (of which our expanding universe is not one), there is no well-defined global energy that is conserved. But that doesn't mean you can make a perpetual motion machine or get free energy from nothing. All it means is that general curved spacetimes don't have a certain mathematical property that many physicists think it would be "nice" to have.

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)?

No. These are all local processes and, as above, local energy conservation holds in GR. For example, the energy radiated away as a bound system (say a star) forms is exactly equal to the decrease in the externally measured mass of the system.

in some articles about the study of galaxies and clusters evolutions and formations, sometimes the effects of the "tidal force" from spacetime expansion is considered

Can you give a reference?

 

[kimbyd]

This is a good blog post that talks about the lack of conservation of energy in General Relativity:
https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/