**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 1.68*X* = 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.