## Ned Wright’s Dark Energy Piston

Since Ned Wright picked up on the fact that I borrowed his famous Dark Energy Piston for my talk I thought I’d include it here in all its animated glory to explain a little bit better why I think it was worth taking the piston.

The two important things about dark energy that enable it to reconcile apparently contradictory observations within the framework of general relativity are: (i) that its energy-density does not decrease with the expansion of the Universe (as do other forms of energy, such as radiation); and (ii) that it has negative pressure which, among other things, means that it causes the expansion of the universe to accelerate.

The Dark Energy Piston (above) shows how these two aspects are related. Suppose the chamber of the piston is filled with “stuff” that has the attributes described above. As the piston moves out the energy density of dark energy does not decrease, but its volume does, so the total amount of energy in the chamber must increase. Since the system depicted here consists only of the piston and the chamber, this extra energy must have been supplied as work done by the piston on the contents of the chamber. For this to have happened the stuff inside must have resisted being expanded, i.e. it must be in tension. In other words it has to have negative pressure.

Compare the case of “ordinary” matter, in the form of an ideal gas. In such a case the stuff inside the piston does work pushing it out, and the energy density inside the chamber would therefore decrease.

If it seems strange to you that something that is often called “vacuum energy” has the property that its density does not decrease when it subjected to expansion, then just consider that a pretty good definition of a vacuum is something that, when you do dilute it, you don’t any less!

So how does this dark vacuum energy stuff with negative pressure cause the expansion of the Universe to accelerate?

Well, here’s the equation that governs the dynamical evolution of the Universe:

I’ve included a cosmological constant term (Λ) but ignore this for now. Note that if the pressure p is small (e.g. how it would be for cold dark matter) and the energy density ρ is positive (which it is for all forms of energy we know of) then in the absence of Λ the acceleration is always negative, i.e. the universe decelerates. This is in accord with intuition: because gravity always pulls we expect the expansion to slow down by the mutual attraction of all the matter. However, if the pressure is negative, the combination in brackets can be negative so can imply accelerated expansion.

In fact if dark energy stuff has an equation of state of the form p=-ρc2 then the combination in brackets leads to a fluid with precisely the same effect that a cosmological constant would have, so this is the simplest kind of dark energy.

When Einstein introduced the cosmological constant in 1915/6 he did it by modifying the left hand side of his field equations, essentially modifying the law of gravitation. This discussion shows that he could instead have modified the right hand side by introducing a vacuum energy with an equation of state p=-ρc2. A more detailed discussion of this can be found here.

Anyway, which way you like to think of dark energy the fact of the matter is that we don’t know how to explain it from a fundamental point of view. The only thing I can be sure of is that whatever it is in itself, dark energy is a truly terrible name for it.

I’d go for “persistent tension”…

### 11 Responses to “Ned Wright’s Dark Energy Piston”

1. I suppose an analogy with the Dirac sea, where the particle-antiparticles pairs have not the antiparticle counterpart and instead the associated energy which causes the expansion like a curvature in the space-time. The energy balance cause the expansion with the curvature, and exist only particles and expansion-curvature.

• telescoper Says:

The Dirac Sea is a good example of how badly wrong the calculation of vacuum energy from first principles can be: if all the negative energy states are filled in a normal vacuum then the vacuum energy is formally negative and infinite..

• domenico Says:

I am thinking that if the undetected antimatter is the expansion curvature, and since the curvature is chargeless and spinless, then the Big Bang could be a chargeless boson (spin 0 singlet, with the same number of positive and negative charges). Is it possible to measure these features from cosmic microwave background? If there are different expansion curvatures from different directions, then there was different density of the galaxies (low density, low redshift).

2. Whats wrong with “vacuum energy”? But I do like “persistent tension”. In fact, the longer things go on, the worse the tension gets. This is also a metaphor for the mystery of dark energy itself.

• telescoper Says:

I don’t like “vacuum energy” because every time I encounter that phrase it reminds me that I should get off my arse and hoover the carpets.

• How about “Boycott Energy”, as with no apparent activity, nonetheless over time, runs mysteriously accumulate. At least that would mystify our American chums.

3. Einstein didn’t try to accelerate the Universe, just to stabilize it. He may have called this a mistake (at least according to Gamov), but he had a brilliant grasp of the possibilities. Is he now a discontent?

4. Will Sutherland Says:

I don’t really get all the complaining about why “dark energy” is such a bad name. Everyone needs a 2-word phrase for the stuff, and “vacuum energy” is too closely associated with Lambda.

I should own up that I have a small share of responsibility for propagating the name, as follows:
the first refereed paper in print with “dark energy” in the title was Perlmutter, Turner and White, 1999, Phys Rev Lett, at link here . (Another paper by Huterer and Turner, PRD 1999, was submitted earlier, but appeared in print later; plus a couple of conference proceedings around the same time).

The above P+T+W paper had 2+1 referees : referees A+B (identities not known to me) disagreed, with A recommending acceptance and B recommending straight rejection.
The editors of Phys Rev Lett then sent it to me as referee C, including the anonymous reports from A+B.
I sent back a report saying effectively that the paper looked good, I agreed with referee A while the criticisms from referee B were either barely relevant or plain wrong, and the editors decided to publish the paper.

It is interesting that none of those three referee reports made any comment about the use of “dark energy”, so it must have seemed reasonably self-explanatory even back in 1999.
So, I suppose I’m peripherally responsible for allowing the “dark energy” name into the literature, but it is not weighing heavily on my conscience.

• Will Sutherland Says:

Sean Carroll: Everything has energy, and many things are dark.
True, but the word-pair “dark energy” seems intuitively clear as per previous comment.

Re “dark flow” – I agree the observational reality is dubious but “nonsense” is a bit harsh. However your last point about not worrying is the opposite of reality, i.e. putting “dark” is probably helpful re publicity/funding/etc.
On a related topic, having “energy” in there probably helps to get funding out of the US Dept of Energy (e.g. the LSST Camera) which might have been more difficult with a different word. I don’t know if Mike Turner planned that, but he might have done.

Finally do we need a name before deviations are found ? I’d say obviously yes, e.g. the neutrino, the Higgs boson, black holes, etc etc , were all named many years/decades before they were actually found. The probabilty of actually finding deviations from a cosmological constant. may not be so high, but we still need a name.

5. telescoper Says:

I found a large number of identical comments from you in the spam filter. I pulled one out but didn’t have time to wade through the others.

6. Hipnotic