Observationally Indistinguishable Dark-Energy Theories

Fundamentally different theories of dark energy may be underdetermined by observation, according to a recent preprint by Sanil Unnikrishnan.

Background. Dark energy was first proposed as a solution to the problem of cosmic acceleration. That is, if you propose the existence of an exotic form of matter (generically labeled “dark energy”), you can account for the observed FRW-expansion, as well as for the late-time ISW effect. However, there is now a whole zoo of different ideas about what dark energy is and what it’s like: quintessence, k-essence, “phantom” energy, or even tachyons — objects travelling at super-luminal speeds. (Here’s a nice review of some of the options, by Sean Carroll.)

The Result. Whatever the nature of dark energy, the only observational access we currently have to it is through its effect on cosmic acceleration. This effect is determined by (global) parameters: the ratio of pressure to density of dark energy, and the ratio of pressure-fluctuations to density-fluctuations.

But what if there were two distinct models of dark energy that gave the same values for these parameters? Then those two models would be indistinguishable by observation. This is the situation that Unnikrishnan argues that we are in. In short: suppose dark energy is modeled as a scalar field (as it is in most of the above proposals). Then any values for these two parameters that you might measure can be derived from distinct scalar field Lagrangians — different models of dark energy.

Some Implications. This would appear to lead to an epistemological quandary. Dark energy is being proposed as a fundamental feature of our universe. So it would be very fishy indeed if the fundamental nature of dark energy were in principle unknowable.

However, the underdetermination isn’t quite as bad as that. If dark energy is what the physics community ends up accepting, then it’s unlikely that our current observational access to dark energy is all we’ll ever get. For example, if we ever succeeded in making any kind of local observation of dark energy in the lab or solar system, then we’d have new dark energy parameters to measure, which would not be underdetermined by this trick.

Furthermore, there are plenty of excuses for cosmic acceleration that don’t model dark energy as a scalar field — for example, those in which a cosmological constant is added to the field equations, and those which model it as the result of early-universe inhomogeneities.

Still, one can’t help but feel a bit uneasy about the whole dark energy program. Historically, it looks a bit too much like Descartes’ vortices — and results like this one don’t make us feel any better.

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