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8. Cosmology III: The Cosmological Parameters
Table 8.2. Cosmological parameters, as derived from the
CMB data (WMAP) and the combination of these with the
data from 2dFGRS and the Lyα forest. Here, z ion is the redshift
of the reionization of the Universe (where it is assumed
that the reionization was homogeneous, instantaneous and
complete), z rec is the redshift of the recombination (this is
the redshift at which the z-distribution of the last scattering
of CMB photons has its maximum), z eq is the redshift where
matter and radiation had the same energy density, n b is the
number density of baryons today, and η is the number density
ratio of baryons to photons (from Spergel et al., 2003, ApJS,
148, 175)
WMAP
WMAPext+2dFGRS+Lyα
h 0.72 ± 0.05 0.71 −0.03
+0.04
σ 8 0.9 ± 0.1 0.84 ± 0.04
σ 8 Ωm 0.6 0.44 ± 0.10 0.38 −0.05
+0.04
Ω b 0.047 ± 0.006 0.044 ± 0.004
Ω m 0.29 ± 0.07 0.27 ± 0.04
t 0 13.4 ± 0.3 Gyr 13.7 ± 0.2Gyr
z ion 17 ± 5 17± 4
z rec 1088 +1
−2 1089 ± 1
z eq 3454 +385
−392 3233 +194
−210
n b (2.7 ± 0.1) × 10 −7 cm −3 (2.5 ± 0.1) × 10 −7 cm −3
η
(
6.5 +0.4
−0.3
scales. We obtain
)
× 10 −10 (
6.1 +0.3
−0.2
)
× 10 −10
Ω ν h 2 < 0.0076 , (8.28)
with a 2σ significance, which implies a strict upper limit
for the neutrino mass of m ν < 0.23 eV, where (4.63) was
used. This limit is significantly tighter than that which
is currently achievable in laboratory measurements. Besides
the Lyα forest, cosmic shear can also be utilized
for measurements on small scales, as is demonstrated in
Fig. 8.34.
8.7.2 Cosmic Harmony
With the exception of the high optical depth τ, the
WMAP results to data have not brought big surprises.
However, this fact in itself is surprising: given the high
sensitivity and angular resolution of this satellite, it
could well have been possible that the measured fluctuation
spectrum showed discrepancies with respect to
our standard model. Remarkably, this does not seem to
be the case.
Hence we are in a situation in which the basic cosmological
parameters are not only known with an accuracy
Fig. 8.34. This figure illustrates the complementarity of the
CMB data with those from cosmic shear. The individual confidence
regions of both methods (blue for the CMB, orange
forcosmicshear)intheΩ m –σ 8 plane are nearly orthogonal,
so that a combination of both methods leads to a significantly
smaller region (green) of allowed parameter pairs
that had been unimaginable only a few years ago, but
also each of these individual values has been measured
by more than one independent method, confirming
the self-consistency of the model in an impressive
manner.
• Hubble Constant. H 0 has been determined with the
Hubble Key Project, by means of the distance ladder,
particularly using Cepheids. The resulting value
is in outstanding agreement with that derived from
CMB anisotropies. Other estimates of H 0 yield comparable
values. Although the determination of H 0 by
means of the time delay measurement for galaxyscale
gravitational lenses, and by means of the SZ
effect typically yield somewhat smaller values, these
are still compatible with the values from the Hubble
Key Project and the CMB measurements within the
range of the expected statistical errors and systematic
effects which are difficult to control.
• Contribution of Baryons to the Total Density. The
ratio Ω b /Ω m has been determined from the baryon
fraction in clusters of galaxies, from redshift surveys,
and from the CMB fluctuations, all yielding
Ω b /Ω m ≈ 0.15.
• Baryon Density. The value for Ω b h 2 determined
from primordial nucleosynthesis combined with