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Aug31-08, 07:36 AM
PF Gold
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P: 522
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.

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.