Energy conservation in dark energy

 Am I right in imagining that the way dark energy seems to increase itself while the rest of the universe remains constant implies that conservation doesn't apply to it but just to the rest?

Yes—with an important qualification. Your intuition is pointing at a genuinely strange feature of cosmology, but I’d phrase it slightly differently.

As the universe expands, ordinary matter and radiation dilute: the same amount of stuff occupies an increasingly large volume. Dark energy, in the simplest cosmological-constant picture, behaves differently: its energy density stays approximately constant. So as space expands, there is more volume containing the same density of dark energy, meaning the total amount of dark-energy associated with that volume increases.

That sounds like energy conservation has gone out the window—and in a sense, there isn't a universal "total energy of the expanding universe" that has to remain constant.

The subtle point is that conservation of energy in general relativity is a local law. In a spacetime with the appropriate symmetry, you can define a conserved energy globally, but an expanding universe doesn't generally have the sort of time-translation symmetry that gives you the familiar global conservation law.

So it isn't quite:

"Conservation applies to everything except dark energy."

Rather:

The usual global bookkeeping rule that says energy cannot increase doesn't apply to the universe as a whole in an expanding spacetime.

And dark energy makes this especially conspicuous. If you take a comoving region of space, its dark-energy density remains constant while its volume grows, so its dark-energy content grows. There isn't necessarily some other reservoir from which that extra energy has been taken.

There's an amusing parallel with cosmological redshift. Photons lose energy as the universe expands—their wavelengths stretch—but that "lost" energy doesn't necessarily go somewhere else. Asking where did it go? assumes a global conservation bookkeeping system that general relativity doesn't provide for the expanding universe.

So your basic instinct is good: dark energy exposes a limitation of the ordinary conservation-of-energy intuition particularly dramatically. But it isn't that dark energy gets a special exemption while matter obeys the rule. The underlying rule itself is more subtle in an expanding universe.

It seems thought that since the energy density remains constant, there would be no way to make practical use of this.

Exactly. That's the catch.

If dark energy has a constant energy density, then expanding space doesn't give us a useful energy gradient to exploit. Imagine a gigantic tank filled with a fluid whose density is exactly the same everywhere. Making the tank larger gives you more fluid, but there's no downhill direction for a turbine to exploit. You don't get useful work merely because there is more of it.

Dark energy is even more frustrating than that analogy suggests. We don't know of any mechanism by which you could make a machine interact with the cosmological constant and extract its energy. It doesn't appear to form clumps, flow, or develop locally exploitable differences in density.

And there's an interesting distinction here: the universe can acquire more dark-energy content without that constituting an energy source. The extra energy comes along with the changing spacetime geometry. It isn't sitting there as a stash of increasingly accessible fuel.

So your thought leads to a rather nice conclusion:

The failure of global energy conservation in cosmology does not amount to a free-energy loophole.

If dark energy were instead something whose density changed in a way that produced usable gradients, things could get much more interesting. But a cosmological constant is remarkably useless stuff—energetically abundant on cosmic scales, yet apparently completely inaccessible.

If the universe is endless in extent, then one might say that the total energy doesn't really increase, just its relationship to other forms of energy.

Yes—and that's actually a very good way of putting your finger on the conceptual problem.

If the universe is spatially infinite, then the total amount of dark energy was already infinite at any earlier time, assuming a nonzero constant density. After expansion it is still infinite. So saying that its "total energy increases" becomes mathematically rather empty: ∞ before and ∞ after.

What changes in a meaningful way is the energy per unit volume relative to the other components. Matter density falls as the universe expands, radiation falls even faster, while dark-energy density stays roughly fixed. Consequently, dark energy goes from being negligible to becoming the dominant component.

There's an even nicer way to express it. Take a fixed comoving volume—say, a region defined by galaxies that expand along with the Hubble flow. Its physical volume increases. Inside it:

• matter: roughly a fixed amount, increasingly diluted;

• radiation: fixed photon count, but each photon also loses energy through redshift;

• dark energy: energy density stays fixed, so the amount attributed to that expanding region increases.

For an infinite universe, though, the global total is not a particularly useful quantity. And even for a finite region, general relativity doesn't give us a simple universal conservation account in an expanding spacetime.

So I think your formulation is better than the naive "dark energy is being created." What is physically significant is the changing composition of the universe, not necessarily an increase in some meaningful global energy total.

And there's a delightful irony here: dark energy doesn't become dominant because it gets stronger. Everything else gets weaker while it stubbornly stays the same.