While I understand the historical significance of [tex][\Lambda][/tex] in respect of Einstein’s initial reluctance to accept the idea of an expanding universe, I am not sure I understand the need to perpetuate its use today. In part, my earlier postings are an attempt to understand whether a basic model of the universe can be described in terms of an energy density plus an associated pressure without recourse to any other symbolic references, e.g. [tex][\Lambda][/tex]?

In post #3, I tried to outline my understanding of the relationship between energy density and pressure in connection with the stability of a star, which might be summarised for reference by way of 2 numbered bullets:

*1. Any volume of space that contains energy must be considered to have an associated mass by virtue of [tex]E=mc^2=hf [/tex] and, as such, this effective mass must have a gravitational effect. *

2. Equally, any volume of space that contains energy must also be considered to have a pressure by virtue of the relationship [tex]P=\omega \rho c^2[/tex].
While possibly overly simplistic, it might be said that the cosmology model is based on just 3 equations, i.e. Friedmann, Fluid and Acceleration, which are often presented with a [tex][\Lambda][/tex] term. However, there are also references that seem able to discuss this model in terms of just energy density and pressure without any direct reference to [tex][\Lambda][/tex], e.g.

http://arxiv.org/abs/astro-ph/0309756
http://relativity.livingreviews.org/...es/lrr-2001-1/
As such, these papers discuss a cosmological model in terms of the following forms of energy density to which there may or may not be an associated pressure:

- Matter = [tex]\rho \propto a^{-3};\ P =\omega \rho c^2;\ \omega =0[/tex]

- Radiation = [tex]\rho \propto a^{-4};\ P =\omega \rho c^2;\ \omega =+1/3[/tex]

- Cold Dark Matter = [tex]\rho \propto a^{-3};\ P =\omega \rho c^2;\ \omega =0 [/tex]

- Dark Energy = [tex]\rho \propto a^{-0};\ P =\omega \rho c^2;\ \omega =-1[/tex]

- Space Curvature = [tex]\rho \propto a^{-2};\ P =\omega \rho c^2;\ \omega =-1/3[/tex]

*Note: Not sure whether CDM follows the same profile as matter?*
If we try to reconcile the description of bullets (1) and (2) within an expanding universe, as described by the Friedmann equations, it seemed logical to initially consider the associated pressure [P] as a source of expansion and energy density as a source of gravitational mass resulting in a slow down of expansion. This is why the value of [tex][\omega_{radiation}=+1/3][/tex] for radiation was questioned in post #4, because it seems to imply that the pressure of radiation actually contributed to the slow down of the earlier universe, not its expansion.