10.2. The equation of state of the vacuum

So far, we have assumed that the vacuum energy is exactly a classical , 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 p_v / _v - 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, _m) space that is required for a given value of h if the location of the main CMB acoustic peak is known exactly. For h 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 _mh = 0.18. In order to match the data with w closer to zero, _m 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 .

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