Hi McHeathen,
I am also looking for some answers about dark energy in terms of its energy density, negative pressure and any gravitational effects, so I hope you don’t mind if I append some additional issues to yours.
From general reading I get the impression that dark energy acts as an effective anti-gravity in that it is said to expand space and push things apart by virtue of its negative pressure. However, I am not sure whether this implies that dark energy is also negative, i.e. like potential energy (?), therefore has negative effective mass by virtue of E=mc^2 and negative pressure is really the net result of anti-gravity?
I have appended some equations and issues linked to the Wikipedia page on the Friedmann equations for further reference and clarification. Thanks
http://en.wikipedia.org/wiki/Friedmann_equations
On the assumption that dark energy equates to the cosmological constant in the Friedmann equation, it seems possible to make the following assumptions about its energy density based on the equivalence of units in the Friedmann equation, i.e.
[1] \rho_\Lambda \equiv \frac {\Lambda c^2}{8 \pi G}
As an aside, the units of Lambda are 1/metres^2, does this suggest some correlation to the radius of the visible universe (?)
Given that energy density is energy per unit volume and any energy can be equated to mass via Einstein’s equation, does this suggests that dark energy must have some sort of effective mass? However, I am not sure whether this scalar quantity is considered positive or negative, especially in light of the following pressure and energy density relationship?
[2] P = \omega \rho c^2 where \omega_\Lambda= -1
Equation [1] allows the cosmological constant in Friedmann’s equation to be replaced by an equivalent energy density. E=mc^2 suggests that dark energy must have an effective mass by virtue of its energy density and therefore some sort of gravitational effect, but I am not sure of the sign of this energy. In contrast, equation [2] seems to suggest that the energy density and pressure must be of different sign due to the sign of omega [w].
Consequently, I am having problems resolving the implied direction of [H] in the Friedman equation plus similar problems with the Fluid equation, which only references energy density with no direct inference to pressure. The Acceleration equation is offset by a pressure factor [\rho + 3P] that seems to allow [-P] to overcome energy density giving a net positive acceleration, however I am not sure that I have a clear picture as to what is really implied here.
