Model Testing and Parameter Estimation 189of a scalar field (E for electric) and the curl of a vector field (B for magnetic). The
source of the E-modes is Thomson scattering. The sources of the B-modes are gravita-
tional waves entailing tensor perturbations, and E-modes which have been deformed
by gravitational lensing of large-scale structures in the Universe.
In analogy with Equation (8.21), the polarization multipole components are
푎E퓁푚=1
푇 0 ∫
dn푃ab(n)푌퓁E푚ab∗(n), (8.39)푎B퓁푚=^1
푇 0 ∫
dn푃ab(n)푌퓁B푚ab∗(n). (8.40)The three sets of multipole moments푎T퓁푚,푎E퓁푚and푎B퓁푚fully describe the temperature
and polarization map of the sky; thus, they are physical observables. There are then
six power spectra in terms of the multipole components: the temperature spectrum in
Equation (8.22) and five spectra involving linear polarization. The full set of physical
observables is then
퐶퓁T=⟨
푎T퓁∗푚푎T퓁′푚′
⟩
,퐶E퓁=
⟨
푎E퓁∗푚푎E퓁′푚′
⟩
,퐶퓁B=
⟨
푎B퓁푚∗푎B퓁′푚′
⟩
,
퐶퓁TE=
⟨
푎T퓁∗푚푎E퓁′푚′
⟩
,퐶퓁TB=
⟨
푎T퓁∗푚푎B퓁′푚′
⟩
,퐶퓁EB=
⟨
푎E퓁푚∗ 푎B퓁′푚′
⟩
}
(8.41)
For further details on polarization, see Kosowsky [9].
Thus polarization delivers six times more information than temperature alone, but
it is much more difficult to observe since the intensity of polarization is so much
weaker than that of temperature.
The first observations of the polarization spectra퐶퓁Eand퐶퓁TEwere made by the
South Pole-based Degree Angular Scale Interferometer DASI [10] and the WMAP
satellite [7]. We refer to the more recent Planck mission results on E-mode polar-
ization and the South Pole-based BICEP2 telescope results on B-mode polarization
[8] in the next section.
8.4 Model Testing and Parameter Estimation
In this section we shall quote best estimators of many cosmological parameters with
‘reliable’ statistical and systematic errors. One may pause to reflect whether that
indeed is possible. The problem is that different nonstochastic systematic errors com-
ing from differences in instruments, selections, Monte Carlo modeling, restrictions of
the parameter space by different priors and so on, can often not be evaluated and, even
less, combined. Moreover, we have only one Universe with its own cosmic variance.
Particle physicists also face the problem of how to combine statistical and system-
atic errors, and they have some receipts for it.
However, the community of astronomers and astrophysicists is not going to accept
any average, because it is not in their culture.
The philosophy of their culture is that the best value comes from one best
measurement.
The set of preferred parameter values always shift by some fraction of휎depending
on the formulations of the theory, and independently of what data sets are included.