10.3. The total relativistic density

Finally, an interesting aspect of figure = is that it reminds us of history. When the COBE detection was announced in 1992, a popular model was `standard' CDM with _m = 1, h = 0.5. As we see, this comes close to fitting the CMB data, and such a model is not unattractive in some ways. Can we be sure it is ruled out? Leaving aside the SNe data, one might think to evade the 2dFGRS constraint by altering the total relativistic content of the universe (for example, by the decay of a heavy neutrino after nucleosynthesis). Since 2dFGRS measures the horizon at matter-radiation equality, this will be changed. If the radiation density is arbitrarily boosted by a factor X, the constraint from LSS becomes

(163)

Therefore X 8 is required to allow an Einstein-de Sitter universe.

However, this argument fails, because it does not take into account the effect of the extra radiation on the CMB. As argued above, the location of the acoustic peaks depends on a_eq, which depends on _m. However, if we change the radiation content, then what matters is _m / X. Thus, the CMB peak constraint now reads

(164)

when combining LSS and CMB, everything is as before except that the effective Hubble parameter is h / X^1/2. Thus, a model with _m = 1 but boosted radiation would only fit the CMB with h 0.5 1.4, and the attractiveness of a low age is lost. In any case, combining LSS and CMB would give the same _m 0.3 independent of X, so it is impossible to save models with _m = 1 by this route.

Finally, it is interesting to invert this argument. Since Percival et al. (2002) obtain an effective h of 0.665 ± 0.047 and Freedman et al. (2001) measure h = 0.72 ± 0.08, we deduce

(165)

This convincingly rules out the 1.68X = 1 that would apply if the universe contained only photons, and amounts to a detection of the neutrino background. In terms of the number of neutrino species, this is N = 3.6 ± 1.1. A more precise result is of course obtained from primordial nucleosynthesis, but this applies at a much later epoch, thus constraining models with decaying particles.