The notion of dark energy is peculiar, even by cosmological standards.
Cosmologists have foisted the idea upon us to explain the apparent accelerating expansion of the Universe. They say that this acceleration is caused by energy that fills space at a density of 10-10 joules per cubic metre.
What’s strange about this idea is that as space expands, so too does the amount of energy. If you’ve spotted the flaw in this argument, you’re not alone. Forgetting the law of conservation of energy is no small oversight.
I like to think that, if I were not a professional cosmologist, I would still find it hard to believe that hundreds of cosmologists around the world have latched on to an idea that violates a bedrock principle of physics, simply because they “forgot” it. If the idea of dark energy were in conflict with some other much more fundamental principle, I suspect the theory would be a lot less popular.
But many people have just this reaction. It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity. (With caveats to be explained below.)
The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.
It’s not that all hell has broken loose; it’s just that we’re considering a more general context than was necessary under Newtonian rules. There is still a single important equation, which is indeed often called “energy-momentum conservation.” It looks like this:
{refer to article}
The details aren’t important, but the meaning of this equation is straightforward enough: energy and momentum evolve in a precisely specified way in response to the behavior of spacetime around them. If that spacetime is standing completely still, the total energy is constant; if it’s evolving, the energy changes in a completely unambiguous way.
In the case of dark energy, that evolution is pretty simple: the density of vacuum energy in empty space is absolute constant, even as the volume of a region of space (comoving along with galaxies and other particles) grows as the universe expands. So the total energy, density times volume, goes up.
This bothers some people, but it’s nothing newfangled that has been pushed in our face by the idea of dark energy. It’s just as true for “radiation” — particles like photons that move at or near the speed of light. The thing about photons is that they redshift, losing energy as space expands. If we keep track of a certain fixed number of photons, the number stays constant while the energy per photon decreases, so the total energy decreases. A decrease in energy is just as much a “violation of energy conservation” as an increase in energy, but it doesn’t seem to bother people as much. At the end of the day it doesn’t matter how bothersome it is, of course — it’s a crystal-clear prediction of general relativity. And one that has been experimentally verified! The success of Big Bang Nucleosynthesis depends on the fact that we understand how fast the universe was expanding in the first three minutes, which in turn depends on how fast the energy density is changing. And that energy density is almost all radiation, so the fact that energy is not conserved in an expanding universe is absolutely central to getting the predictions of primordial nucleosynthesis correct. (Some of us have even explored the very tight constraints on other possibilities.)
Having said all that, it would be irresponsible of me not to mention that plenty of experts in cosmology or GR would not put it in these terms. We all agree on the science; there are just divergent views on what words to attach to the science. In particular, a lot of folks would want to say “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.” Which seems pretty sensible at face value.
There’s nothing incorrect about that way of thinking about it; it’s a choice that one can make or not, as long as you’re clear on what your definitions are. I personally think it’s better to forget about the so-called “energy of the gravitational field” and just admit that energy is not conserved, for two reasons.
First, unlike with ordinary matter fields, there is no such thing as the density of gravitational energy. The thing you would like to define as the energy associated with the curvature of spacetime is not uniquely defined at every point in space. So the best you can rigorously do is define the energy of the whole universe all at once, rather than talking about the energy of each separate piece. (You can sometimes talk approximately about the energy of different pieces, by imagining that they are isolated from the rest of the universe.) Even if you can define such a quantity, it’s much less useful than the notion of energy we have for matter fields. The second reason is that the entire point of this exercise is to explain what’s going on in GR to people who aren’t familiar with the mathematical details of the theory. All of the experts agree on what’s happening; this is an issue of translation, not of physics. And in my experience, saying “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” does not actually increase anyone’s understanding — it just quiets them down. Whereas if you say “in general relativity spacetime can give energy to matter, or absorb it from matter, so that the total energy simply isn’t conserved,” they might be surprised but I think most people do actually gain some understanding thereby.
Energy isn’t conserved; it changes because spacetime does. See, that wasn’t so hard, was it?
From the site of cosmologist/theoretical physicist Sean Carroll
https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
He has some special formatting for equations and stuff that can’t be easily copied over, so check the site if you’re looking for that
So I understand you may be looking for an article saying "energy is not conserved" but what you found was an article about how both can be true depending on definitions. His preferred language is:
but this is giving/absorbing spacetime identical to according a ZPE field to spacetime that receives energy (such as from redshift) and releases energy (such as to the background field). Which is conservation.
The problem he cites at the beginning is a biggie, across the field, not something that qualifies his view as better or another as worse. More simply it's the idea that some observation suggests there's a giant energy field holding everything together and other observation suggests this field is excessively generally uninterested in working with things, which seem to be contradictory behaviors for the same energy, which can be quantified as many orders of magnitude apart.
My basic solution, though I don't have all of it and am still studying, is that the variability of certain "constants" changes the timescale and removes the calculation errors that lead to the discrepancy. (This also removes the need for imagining dark energy out of nowhere.)
His proposal doesn't solve the problem either, though, it merely attempts to improve the description so that we can get around to solving the problem of why the zero-point energy appears massive.
Now, cutting to the chase, what everyone wants to know is how miracles get done. The answer is that they arise by tapping the hidden energy of the universe, not by breaking laws of conservation but by opening up yet-unexplained phenomena that access that energy. Scientists and theologians are scrambling over each other trying to get control of that phenomenon, but it's elusive for a reason and knowledge will proceed according to plan. Whether we define miracles as conservative (as I do) or as nonconservative (as OP does) won't matter as long as the definition accords with the data.
And my point has been that all scientific observations have problems that don't complete the explanation of the data, and that this proves the universe is not closed but instead contained. And for that purpose we'd conclude that there is something that doesn't follow conservation somewhere in the system until we define it better. For Big Bang Theory, that lack of following, that connection to the container, is found in the first Planck instant. Maybe Carroll is defining other connections to the container (which theologians would call "providence") but he still follows the general rule of leaving the universe open to a Creator.