Is energy conserved in an expanding universe?

[Jorrie]

Cosmic static and binding energies?

Thanks pervect.

You've definitely computed some sort of number. The physical significance of this number is somewhat questionable. You might want to question why you consider this number to represent any sort of "energy".

I understand that 'rest energy' in this context is problematic but why I considered 'this number to represent any sort of "energy"' is probably not so problematic. Since we know the co-moving size and the critical energy density of the observable universe, we can easily calculate a present 'static' energy component of 2.62E+71 Joule for the observable universe. Is it not reasonable to say that this number represents some valid component of the total energy?

OK, the frame dependence remains, but it may be valid in our 'observational frame', whatever that means. Anyway, the next step could be to calculate the negative gravitational binding energy from this value. You said:

Another thing missing from your formula for "energy" would be any concept of "gravitational binding energy". For instance, the Newtonian gravitational binding energy of a sphere of mass M depends on its radius, R, by the formula

E = -G M^2 / r

Based on this and the 2.62E+71 Joule (or 2.92E+54 kg) 'static energy' of the observable universe and taking the co-moving radius as 46 Gly, or 4.35E+26 m, I get a present binding energy of -1.30E+72 Joule.

If this is correct, can one then conclude that the positive energy of expansion (the 'kinetic' energy?) is 1.30E+72 Joule, so that the total (binding + expansion) energy of the observable universe is zero for the Omega=1 case?

If all the above make any sense, (which I doubt somehow) one can calculate the variable static and expansion energies over the history of the universe as per the attached graph. This is an "engineering approach", which I hope is not considered too "agricultural"!

 

[pervect]

OK, the frame dependence remains, but it may be valid in our 'observational frame', whatever that means. Anyway, the next step could be to calculate the negative gravitational binding energy from this value. You said:

If this is correct, can one then conclude that the positive energy of expansion (the 'kinetic' energy?) is 1.30E+72 Joule, so that the total (binding + expansion) energy of the observable universe is zero for the Omega=1 case?

If all the above make any sense, (which I doubt somehow) one can calculate the variable static and expansion energies over the history of the universe as per the attached graph. This is an "engineering approach", which I hope is not considered too "agricultural"!

How to put this: I would not recommend trying to get the above analysis published in a peer-reviewed journal

Note that the formula I gave for binding energy was a Newtonian formula - not a GR formula. As I have been trying to explain, a GR formula just doesn't exist, at least not for the case of the universe - there are many situations in which GR does define an energy, the universe as a whole happens not to be one of them.

So you're (slightly) better off not including the binding energy rather than applying a Newtonian formula in an area where you know it won't give the right answer. (It would be best if this were a conscious omission). But basically the whole approach is so badly flawed as to be not worth very much, and if you talk to anyone knowledgeable about GR about the "energy of the universe" you shouldn't be too surprised if you get negative reactions or "funny looks".

 

[Jorrie]

So you're (slightly) better off not including the binding energy rather than applying a Newtonian formula in an area where you know it won't give the right answer. (It would be best if this were a conscious omission). But basically the whole approach is so badly flawed as to be not worth very much, and if you talk to anyone knowledgeable about GR about the "energy of the universe" you shouldn't be too surprised if you get negative reactions or "funny looks".

OK, thanks again, I expected something to this effect.

One final question: if I drop the 'observable universe' as a basis and just consider a large, finite region that is fairly homogeneous, would the [edit: 'evolution over time of the'] 'static energy' (including all forms) still be fundamentally flawed as a concept?