It's not. Moreover, the total energy is actually being lost, as particles "lose" kinetic energy due to expansion (and the light is red-shifted).
If this seems to violate the law of energy conservation, you're spot on. It is indeed being violated.
This is not fundamentally problematic by itself, because the law of conservation of energy depends on time invariance. Which doesn't hold in the case of an expanding universe. But it is an unsatisfying copout, and we hope that it can be resolved by the quantum gravity.
No, it doesn't, because the concept of "gravitational potential energy" is not meaningful for an expanding universe considered as a whole. It's only meaningful for isolated systems within the universe.
Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place?
Which that amount should be increasing as space-time expands.
Thought experiment, if you could place a mass of an arbitrary amount at any one point in space, how much mass would you need such that all the mass of the universe is now falling towards it.
Or could you bend space-time to a point that all mass falls into it.
> Wouldn't there be meaning in saying it would take this much energy to push all the matter in the universe to one place?
No. The universe is not an isolated system that we can operate on from the outside. You can't treat it as though it is. So your thought experiments aren't meaningful.
Obviously the thought experiment requires energy that doesn't 'exist' or doesn't have meaning in the sense that it could happen literally. It's a what-if and that does have a number and that does have meaning.
So there is meaning to the previous persons question which is what the thought experiments were meant to show but obviously that's something you can't imagine.
> Obviously the thought experiment requires energy that doesn't 'exist'
No, it requires energy to be added to the system from outside the system. Which is precisely what you cannot do with the universe as a whole. That's what makes such thought experiments meaningless for the universe as a whole.
Um, what? I can operate on an ordinary volume (say a beaker in my lab or a planet that I am in a distant orbit around) from the outside. I can't operate on the universe as a whole from the outside. How is this not an obvious difference?
If you fix a sub-volume of the universe where the boundaries of the volume are subject to the expansion of space, you can calculate the energy in the volume. The question upthread is clearly "does the energy in this volume increase due to expansion?". I'm not sure why you're so focused on integrating over the entire universe; that wasn't an important part of the question upthread. You are being very vague. If you have a coherent mathematical objection that you are trying to explain indirectly, please just say the mathematical objection.
Why is it not meaningful? "Isolated systems" seems meaningless - there is no objective cutoff where a gravitational system becomes "isolated", except perhaps in the sense of "non-intersecting light cones".
I have read all of your comments and not one of them actually says anything concrete. It's the exact same vague objection repeated over and over again.
Please explain exactly why you think calculating the total gravitational potential energy of the entire universe or a well-defined sub-volume of it is intractable. Feel free to use arbitrarily technical mathematical or physics language, just please stop being vague.
Yes, it should increase on paper, but no source of energy to power that expansion is found yet. Big Shrink can power itself, so I'm voting in favor of https://en.wikipedia.org/wiki/Shapley_Attractor
If this seems to violate the law of energy conservation, you're spot on. It is indeed being violated.
This is not fundamentally problematic by itself, because the law of conservation of energy depends on time invariance. Which doesn't hold in the case of an expanding universe. But it is an unsatisfying copout, and we hope that it can be resolved by the quantum gravity.