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10.2. The equation of state of the vacuum

So far, we have assumed that the vacuum energy is exactly a classical Lambda, or at any rate indistinguishable from one. This is a highly reasonable prior: there is no reason for the asymptotic value of any potential to go exactly to zero, so one always needs to solve the classical cosmological constant problem - for which probably the only reasonable explanation is an anthropic one (e.g. Vilenkin 2001). Therefore, dynamical provision of w ident pv / rhov neq - 1 is not needed. Nevertheless, one can readily take an empirical approach to w (treated as a constant for a first approach).

Figure 22 shows a simplified approach to this, plotting the locus on (w, Omegam) space that is required for a given value of h if the location of the main CMB acoustic peak is known exactly. For h appeq 0.7, this is very similar to the locus derived from the SN Hubble diagram (Garnavich et al. 1998). The solid circles show the updated 2dFGRS constraint of Omegamh = 0.18. In order to match the data with w closer to zero, Omegam must increase and h must decrease. The latter trend means that the HST Hubble constant sets an upper limit to w of about -0.54 (Percival et al. 2002). This is very similar to the SNe constraint of Garnavich et al. (1998), so the combined limit is already close to w < - 0.8. The vacuum energy is indeed looking rather similar to Lambda.

Figure 22

Figure 22. The Omegam h3.4 degeneracy for flat models gives an almost exact value of Omegam from the CMB is h is known, assuming the vacuum to be effectively a classical Lambda (w = - 1). If w is allowed to vary, this becomes a locus on the (Omegam, w) plane (similar to the locus for best-fitting flat models from the SNe, showed dotted). Solid circles show values of Omegamh that satisfy the updated 2dFGRS constraint of 0.18 (suppressing error bars).

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