Preposterous Universe

Monday, September 13, 2004
Phantom energy

Last time we talked about dark energy and its equation-of-state parameter, w. This number tells you how quickly the dark energy density changes as the universe expands; if w=-1, the density is strictly constant, if w>-1, the density decreases, and if w<-1, the density actually increases with time. (In equations, if a is the scale factor describing the relative size of the universe as a function of time, then the density goes as a-3(1+w).) For comparison purposes, cosmological "matter" (slowly-moving massive particles) has w=0, and "radiation" (relativistic particles, including photons) has w=1/3.

Einstein's cosmological constant is just the idea that there is a fixed minimum energy density everywhere in the universe; this vacuum energy would correspond to w=-1. It's easy enough to get an energy density that slowly diminishes, with w>-1; all you need to do is invent some scalar field slowly rolling down a very gentle potential, so that the energy is nearly constant but in fact gradually diminishes.

What about w<-1, corresponding to a gradually increasing energy density? It's not what you would typically expect; the expansion of the universe tends to dilute energy, not increase it. So for a some time cosmologists who put observational limits on the value of w would exclude w<-1 by hand. In fact, I am somewhat to blame for this custom. As far as I know, the first paper to constrain w using supernova data is the one by Garnavich et al., the High-Z Supernova Team. I am friends with these guys -- Brian Schmidt, leader of the collaboration, was my officemate during grad school -- and one day they called me up to ask whether there was a good reason why they could ignore w<-1. In general relativity, it often happens that we want to make some general statements about possible solutions without knowing exactly what the matter/energy sources are, so we invoke "energy conditions" that put some reasonable constraints on what the sources can do. The most physically reasonable condition is the Dominant Energy Condition (DEC), which is what allows you to prove that energy can't propagate faster than the speed of light. So I pointed out that imposing the DEC would exclude the w<-1 possibility. I wrote a couple of paragraphs to this effect, and got included as a co-author on the paper; afterwards, people were happily ignoring w<-1 a priori.

Most people, anyway. A notable exception was Robert Caldwell at Dartmouth, who wrote a paper suggesting that w could be less than -1, and built an explicit model. The idea was simple: have a scalar field rolling in a potential, but give it a negative kinetic energy. That means that the field tends to roll up the hill to the top of the potential, rather than rolling down to the bottom. The energy density thus tends to increase, implying w<-1. Caldwell called his idea "phantom energy," both because the Phantom Menace had just come out and also because negative-kinetic-energy fields also appear in the context of quantized gauge theories, where they are called "ghost" fields.

More recently, Caldwell collaborated with Marc Kamionkowski and Nevin Weinberg on the idea of a "Big Rip." If w is less than -1 and constant, the energy density grows without bound and everything in the universe is ripped to shreds at some finite point in the future. This is a fun idea to think about, but some observers took it too seriously, and began phrasing their limits in terms of how many years would have to pass before there would be a Big Rip. That is just silly; even if w<-1, there's certainly no good reason to think it's a constant.

I've gone on too long again. Next time, I promise, I'll talk about my own papers, which are what you really care about, I know. Maybe I'll even talk about what w probably is, in addition to what it is allowed to be.

Ideas on culture, science, politics.
Sean Carroll

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