How Does Dark Energy Exhibit Negative Pressure in Cosmology?

[Rasalhague]

The Wikipedia article on dark energy says "dark energy would need to have a strong negative pressure". In what sense can energy "have" pressure?

Is it that the value of the metric tensor field at an event, when multiplied by the cosmological constant, is a tensor in some way analogous to the stress-energy tensor, with components corresponding to energy-density, momentum density and stress? Is this effectively the stress-energy tensor of some, as yet, unidentified matter? If so, why does it play a different role in the equation to the stress-energy tensor of dark matter, which I'm guessing (rightly or wrongly) is subsumed into the regular stress-energy tensor. When Wikipedia: Dark energy says, "In the standard model of cosmology, dark energy currently accounts for 73% of the total mass-energy of the universe", what is the relationship of pressure to this figure of 73%?

 

[Mentz114]

The dark energy looks like this in terms of SETs. Isotropic negative pressure.

$$G_{\mu\nu}=\kappa \left[ \begin{array}{cccc}<br /> \mu c^2& 0 & 0 & 0 \\\<br /> 0 &0 &0 & 0 \\\<br /> 0 &0 &0 & 0 \\\<br /> 0 & 0 & 0 & 0\end{array} \right]-<br /> \left[ \begin{array}{cccc}<br /> \Lambda g_{00} & 0 & 0 & 0 \\\<br /> 0 &\Lambda g_{11} & 0 & 0 \\\<br /> 0 & 0 &\Lambda g_{22} & 0 \\\<br /> 0 & 0 & 0 & \Lambda g_{33}\end{array} \right]$$

 

[Rasalhague]

What does $\mu$ stand for in the time-time component of $\text{diag}(\mu c^2,0,0,0) = T_{\mu\nu}$? Is the name pressure only given to the spatial diagonal components of the second term? If this is a tensor equation, could we chose coordinates in which the second term on the right, by analogy with the stress-energy tensor, would have off-diagonal space-space components (dark stress)? Does the name dark energy refer to $\Lambda g_{00}$, or to the whole of the second term on the right, or to or $\mu c^2$, or to the whole expression? Does the name dark energy refer to a quantity defined only in a particular conventional coordinate system, or does it refer to a particular component of a tensor, regardless of what value that component takes in a given coordinate system?

 

[Mentz114]

The first term is the SET of the gravitating matter in its rest-frame. The second term is energy/pressure caused by $\Lambda$. The SET of a perfect fluid is

$$T_{\mu\nu}=(\mu+p)U_\mu U_\nu + pg_{\mu\nu}$$

with U_m=0, m= 1,2,3 and U₀ <> 0, it reduces to something like my first expression. So the cosmological constant is claimed to be energy/pressure ( I've dropped a factor of c² somewhere...)

This is informative,

http://en.wikipedia.org/wiki/Fluid_solution

 

[Rasalhague]

Do "gravitating matter" and "perfect fluid" here both refer to the source of the acceleration in the expansion of the universe, commonly called dark energy?

And do I understand you correctly that $\Lambda g_{\mu\nu}$ is just the $p g_{\mu\nu}$ term of the SET for this exotic perfect fluid?

 

[Rasalhague]

Are you referring to this theory: Dark fluid?