Physical Foundations of Cosmology

396 Cosmic microwave background anisotropies

primordial spectrum of gravitational waves produced by inflation, one of the most
challenging predictions to verify.
The polarization of the cosmic microwave background is an inevitable conse-
quence in any model because recombination is not an instantaneous process. The
quadrupole anisotropy of the microwave background, which is absent before re-
combination begins, is produced by both scalar and tensor perturbations as recom-
bination proceeds. In turn, this leads to radiation, scattered off electrons, through
Thomson scattering, being linearly polarized. Note that if recombination were in-
stantaneous, no significant polarization would be generated. Hence, measuring the
polarization gives us a chance to uncover the subtle details of the recombination
history. Note that Thomson scattering on the electrons does not produce any circular
polarization.
Just as with the temperature fluctuations, the most useful quantity to compute is
the two-point correlation function for polarization. The polarization signal is very
weak: it is expected to be only 10% of the total temperature fluctuations on small
angular scales, decreasing to much less than 1% on large angular scales. Hence, as
difficult as it is to detect the temperature fluctuations, detecting the polarization is
an even more extraordinary experimental challenge. Nevertheless, experimentalists
are up to the challenge and the prospects seem to be excellent.

9.10.1 Polarization tensor

The electric fieldEis always transverse to the direction of propagation of the
electromagnetic wave, characterized by the unit vectorn.Therefore, this field can be
decomposed asE=Eaea, wherea= 1 ,2 andeaare two linearly independent basis
vectors perpendicular ton(Figure 9.4).Completely (linearly) polarized light always
has vectorEaligned in a definite direction, while in the opposite case of completely
unpolarized radiation, allEdirections perpendicular tonare equally probable.In
the absence of circular polarization,the radiation polarization properties can be

e 2

e 1

n

E

Fig. 9.4.