Posted: Aug 14, 2010 1:53 am
by Oldskeptic
My decrepit old computer seizes up when trying load pdfs so I can’t take a look at your graphic, but I was able to figure out that it is in an article by Sean Carroll. If you think that Carroll thinks that w can be less than -1, which is what it would take for energy density increasing over time, then you are mistaken. For this to happen energy would have to be able to propagate faster than the speed of light. In fact he says that he contributed to a paper about it.

He does say though that the value of w seems to be centered around -1, which would make the energy density constant if it was exactly -1, but all it would take for energy density to be decreasing is a small difference from -1 to a higher value. And given the rule of thumb that density decreases with expansion this seems to be the likely case.

Sean Carroll:
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. ... nergy.html