Dark Energy: Questions on Uniform Energy Density

[MackBowen]

About a week ago at campus, we had a colloquium on dark energy. I have been studying it some, and a couple of things are bothering me. Perhaps someone can help :)

My worry comes from the idea of uniform energy density. As I understand it, this can be explained either as truly uniform - cosmological constant, or as scalar fields that change slightly. Either explanation seems to have the same two issues.

The first issue is with thermodynamics. If the universe is expanding, and if there is a uniform energy density throughout the universe... this causes issues. The energy has to be coming from somewhere as the volume of the universe increases.

The second one is with relativity. If there is a uniform energy density that permeates the entire universe... well, it seems a lot like the definition of aether to me. It seems that the rest frame of the "dark energy" would be considered a preferred frame of reference, which raises havoc with relativity.I hope someone can clear these issues up for me :)

 

[nicksauce]

Hi MackBowen,

There are two ways, as I see it, to approach the issue of energy conservation in the expanding universe.

The first is Newtonian: The total energy in a certain fluid will change as the universe expands, but this is made up for by doing PdV work in expanding the universe. Example 1: Radiation - Energy density in radiation goes like a^-4, while the volume of the universe goes like a^3, so the total energy in radiation goes down as the universe expands. However, because the radiation fluid has a positive pressure (P=1/3rho), it does work in expanding the universe, which makes up for the lost energy. Example 2: Dark energy. Energy density in DE is constant, so the total energy in dark energy goes up as the universe expands. However, because it has a negative pressure (P=-rho), it does "negative work" in expanding the universe, which makes up for the gained energy.

The better (i.e., more accurate) way to think about it, though, is relativistically. In relativity, global energy conservation is only guaranteed if space-time has a Timelike Killing vector. Our universe doesn't (the FRW metric is time-dependent), so global energy conservation isn't guaranteed. Only local energy conservation (i.e., div(stress tensor)=0) is guaranteed in relativity.

I don't think there is any issue at all with dark energy violating relativity. After all, you can write down all these equations in relativistic form, thus they are compatible with relativity.

 

[bapowell]

The first issue is with thermodynamics. If the universe is expanding, and if there is a uniform energy density throughout the universe... this causes issues. The energy has to be coming from somewhere as the volume of the universe increases.

You are correct. The energy associated with the CC (or dark energy field) is not conserved in a comoving volume. Remember though, energy is not singly conserved in general relativity, rather, it is the stress-energy tensor that obeys a conservation constraint.

The second one is with relativity. If there is a uniform energy density that permeates the entire universe... well, it seems a lot like the definition of aether to me. It seems that the rest frame of the "dark energy" would be considered a preferred frame of reference, which raises havoc with relativity.

Preferred in what sense? It certainly forms a convenient reference frame, but not one of fundamental significance. In fact, we already have such rest frames even without dark energy. Take the CMB for example: it too is uniform to a rather spectacular degree. Observers who are at rest with respect to the expansion of the universe (so-called comoving observers) are also at rest with respect to the microwave background. This forms a convenient reference frame that cosmologists use frequently. For example, the age of the universe is quoted with respect to this frame.