What is this quintessence of dust?

Something I didn’t get around to in last week’s discussion of dark energy and its equation of state parameter was the question of priors — i.e., what do we expect the parameter to be? Physically, this is equivalent to asking how we expect the dark energy to evolve with time, if at all.

We have to admit that there is one special value that the equation of state parameter w might have: namely, w=-1, corresponding to a dark energy density that is strictly constant (equivalent to vacuum energy or Einstein’s cosmological constant). In that case, the dark energy is simply a constant amount of energy that is inherent in each cubic centimeter of spacetime. Any other possibility means that the dark energy density is dynamical, and is presumably obeying some equations of motion. In the comments, Serenus was hoping that I would encourage people to be completely open-minded, and not favor w=-1 over any other value; rather, just collect the data and take the results at face value. In other words, he wants a uniform prior, in which the a priori probability of w=-1 is the same as w=-0.99 or w=-1.01.

Although I hate to disappoint anyone, I can’t agree. The reason is pretty straightforward; I think it was Tolstoy who said, “Cosmological constants are all alike; every model of dynamical dark energy is dynamical in its own way.” Tautological enough, but it points to an important feature of dynamical dark energy candidates — because they have more features than simply their energy density, there are more ways they could be detected and thus more parameters you need to fine-tune to explain why we haven’t noticed them yet.

The simplest example of dynamical dark energy (although by no means the only interesting one) is quintessence, a light scalar field gradually rolling down a potential. Since the field is rolling slowly, the kinetic energy is extremely small and the potential is nearly constant, giving us a nearly-constant energy density, which is just what you want for dark energy. But as soon as you allow for dynamics in this way, there are things you need to explain. For any dark-energy candidate, you need to explain why the energy density is small. But for quintessence, you also need to tell me why it is rolling so slowly; this translates into the fact that the potential must be very shallow, which then translates into the fact that the mass is very small. (The mass is a measure of the curvature of the potential; this is not exactly the same as the slope, but they should be related unless you want to do even more fine-tunings.) In particle physics, masses of scalar fields tend to be very large. The Higgs boson purportedly has a mass of order 1011 electron volts, and a big problem (the “hierarchy problem”) is why this number is so much smaller than the Planck scale, 1027 electron volts.

The quintessence field, meanwhile, would have to have a mass of order the present Hubble constant, about 10-33 electron volts. So if 1011 electron volts is very small, how do we hope to explain 10-33 electron volts?

Once you know the mass is so small, you realize that low-mass particles tend to give rise to observable long-range forces. The two forces we know from our macroscopic experiences are gravitation and electromagnetism, mediated by two zero-mass particles (the graviton and the photon); the nuclear forces are less manifest because they are such short-range. So the quintessence field should give rise to an observable, long-range “fifth force.” The typical way out of this conundrum is to simply declare by hand that the new quintessence field doesn’t interact with ordinary matter, so we can’t feel the force. But this is a cheat; we know that quintessence interacts with gravity, and gravity interacts with ordinary matter, and the miracle of quantum field theory tells us that if A and B both interact with C, then A and B will interact with each other. We can even estimate the strength of this interaction, imagining that it is suppressed by the Planck scale. Then we go look for it, for example in the delicate torsion-balance experiments at the University of Washington. The idea is that the strength of the quintessence force will necessarily be different for objects of different compositions; it’s a rule that only gravity can couple to objects in a way that is completely indifferent to what they are made of. So by looking for tiny anomalous accelerations of, say, Aluminum and Copper in the direction of the Sun, we can put limits on the strength of any purported new long-range forces.

The answer is that we don’t see any such forces, at least not yet. From the upper limits we currently have, the forces must be about 10-5 times less than what you might have expected. That’s pretty small, although not so small (especially given the roughness of the theoretical estimate) that there’s no reason to keep looking.

What’s more, there is another way to constrain the direct interactions of quintessence. If you have a scalar field that is slowly evolving as the universe expands, all of the “constants of nature” tend to change along with it. That’s because what we think of as constants of nature, like the mass of the up quark or Newton’s constant of gravitation, are actually parameters that depend on the quantum state of the universe (just as the speed of sound depends on properties of the medium through which it is traveling). This is interesting, because there are claims that the fine-structure constant, which determines the strength of the electromagnetic interaction, has actually been experimentally observed to be varying with time. Now, to be honest, these measurements are very hard to do, and people have obtained conflicting results, and the most likely situation is that the experiments are simply in error. So there is some possibility that we have actually already detected the signature of quintessence in a time-variation of the fine structure constant, but it’s somewhat safer to simply imagine that we’ve put a good upper limit on any such variation.

All of the above gives some reason to think that a constant vacuum energy is preferable to dynamical dark energy, simply because it makes more sense that we haven’t yet detected any direct interactions (because constant vacuum energy doesn’t have any). This is not really the same thing as just using Occam’s Razor, which is an important principle but usually only reliable when everyone already agrees on what the correct answer is.

Of course, the idea that dynamical dark energy is a simple scalar field is a nice one, but not unique; there are other possibilities. An especially exciting possibility is that the dark energy does have non-trivial interactions, but only with hard-to-detect particles like dark matter or neutrinos. But the moral of the story remains: once you admit the possibility of dynamics, the models generally allow for all sorts of ways to detect them in principle, and you have to do more fine-tunings to explain why the dark energy hasn’t been seen directly. The idea of an absolutely constant vacuum energy (w=-1) is the simplest and most robust; it’s therefore perfectly permissible to imagine that it’s a little more likely than the other possibilities. Personally, I give about a 10% chance that the dark energy is dynamical. But it’s a testable hypothesis, and if you find some variation then you get in line for the Nobel Prize. So even if it’s something of a long shot, it’s well worth looking for.

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