Model Testing and Parameter Estimation 191introduced in Equation 5.20. The results are in agreement with other determinations,
but no longer accurate enough to be of interest.
Reionization. Since polarization originated in the LSS when the horizon was about
- 12 ∘of our present horizon, the polarization fluctuations should only be visible in
multipoles
퓁>60 ∘
1. 12 ∘
≈ 54.
But the CMB experiments also observe a strong signal on large angular scales,
퓁<10. This can only be due to reionization later than LSS, when the radiation on
its way to us traversed ionized hydrogen clouds, heated in the process of gravitational
contraction. The effect of CMB reionization is called theSunyaev–Zel’dovichEffect
(SZE) (Yakov B. Zel’dovich, 1914–1987). As a consequence of the SZE, the CMB spec-
trum is distorted, shifting towards higher energy.
From the size of this spectral shift one estimates a value for the Thomson scattering
optical depthto the effective reionization clouds,휏[6], which is essentially indepen-
dent of cosmological modeling
휏= 0. 09 ± 0. 01 , (8.46)but strongly degenerate with푛s. This corresponds to reionization by an early gen-
eration of stars. One quotes [6] the redshift at which the Universe is half reionized,
푧re= 11 .15. It could still be that this picture is simplistic, the reionization may have
been a complicated process in a clumpy medium, involving several steps at different
redshifts.
CMB Parameters. The parameters required to model CMB are some subset of the
parameters퐻 0 , the observational matter densities훺mℎ^2 and훺bℎ^2 (b for baryuns), the
cosmological constant density훺휆), the optical depth휏, the amplitude퐴of the power
spectrum, the scalar power index푛sin Equation (7.59), the ratio of the tensor to scalar
power index,푟=푛t∕푛s, the energy variation of the scalar index d푛s∕d푘,andthelinear
theory amplitude of fluctuations휎 8 within 8Mpcℎ−^1 spheres at푧=0.
The primordial fluctuations are assumed to be Gaussian random phase, since no
evidence to the contrary has been found.
The first acoustic T peak in Figure 8.3 determines the scale퓁ofthetimewhen
matter compressed for the first time after푡dec. The positions and amplitudes of
the peaks and troughs in the temperature (T) power spectrum Figure 8.3 and the
temperature–polarization (TE) cross-power spectrum in Figure 8.5 contain a wealth
of information on cosmological parameters. The position in퓁-space is related to the
parameters푛s,훺mℎ^2 and훺bℎ^2 The amplitude of the first peak is positively correlated
to훺mℎ^2 and the amplitude of the second peak is negatively correlated to훺bℎ^2 but,
to evaluate the physical matter densities훺m,훺band훺c, one needs to know a value
forℎ, which one can take from Section 1.4. Increasing푛sincreases the ratio of the
second peak to the first peak. At fixed푛s, however, this ratio determines훺b∕훺m.The
amplitudes also determine the effective number of neutrino generations푁effand put
limits on the total mass of the neutrino generations.훺휈ℎ^2.