Preposterous Universe

Friday, September 10, 2004
The dark energy equation of state

As Preposterous readers know all too well, about seventy percent of the stuff in the universe is a mysterious substance called dark energy (unless general relativity is breaking down, which is interesting but less likely). We know only two things about the dark energy: it is spread nearly uniformly throughout space, and its density is nearly constant as a function of time. In other words, it doesn't dilute as the universe expands, unlike the energy in ordinary matter and radiation. So as time goes by, the dark energy becomes more and more dominant, as ordinary stuff becomes increasingly rarefied. (Worried about conservation of energy? Don't be.)

But we don't understand the dark energy that well, so we want to measure its properties as precisely as possible to get clues as to exactly what it might be. The simplest possibility is that it's vacuum energy, or the cosmological constant -- a perfectly constant energy density inherent in the fabric of spacetime itself. But it could also be something dynamical, changing in density gradually as the universe expands. In that case, we can hope to measure how fast its changing by looking at the evolution of the expansion rate of the universe; according to Einstein, the expansion rate (the Hubble constant) is proportional to the square root of the total energy density. We can make this measurement using a variety of cosmological probes -- supernovae, large-scale structure, the evolution of galaxies and clusters, the cosmic microwave background, gravitational lensing, gravitational waves, and more -- and there is a grand multi-pronged program under way to do just that over the next decade or two.

There are an infinite number of ways that some quantity (the energy density of the dark energy, or equivalently the expansion rate of the universe) can change with time, but we don't measure things with infinite precision. So we need to decide how to simply characterize the results of what we measure. Cosmologists have settled on quoting the equation-of-state parameter w, defined as the ratio of the pressure of the dark energy to its energy density. The interesting thing about dark energy is that it has a negative pressure, a/k/a a tension. This isn't so surprising all by itself; a stretched rubber band has tension, too. It's this tension that allows the density to persist as the universe expands. (Said another way, not necessarily more helpfully, the deceleration/acceleration of the universe depends on the energy density plus three times the pressure; so a large negative pressure induces acceleration, while a positive energy density without any accompanying pressure would cause the universe to decelerate.)

The equation-of-state parameter governs the rate at which the dark energy density evolves. For a perfect, unchanging vacuum energy, we have w=-1: the pressure is equal in magnitude and opposite in sign to the energy density. If w is a little bit greater than -1 (e.g., -0.9 or -0.8), the dark energy density will slowly decrease as the universe expands. This would be the case, for example, if the dark energy were the potential energy of some slowly-rolling scalar field (sometimes called "quintessence"). Current experimental bounds tell us that w=-1 is the central preferred value, but there is room for improvement; see the plot at the bottom of Licia Verde's page for the latest results.

This is all preliminary to mentioning the most recent paper I've written, which I'll do in the next post. (For a preview, see these slides from a recent talk [pdf].) If w is less than -1, the energy density of the dark energy is actually increasing as the universe expands. Is this okay? Have cosmologists gone crazy? Stay tuned for our exciting conclusion!

Ideas on culture, science, politics.
Sean Carroll

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