Polarizationpolarization 185anisotropies found correspond to temperature variations of
훿푇= 29 ± 1 휇K, or 훿푇∕푇= 1. 06 × 10 −^5. (8.24)Half of the above temperature variations, or훿푇= 15. 3 μK, could be ascribed to
quadrupole anisotropy at the 90∘angular scale. Although some quadrupole anisotropy
is kinetic, related to the dipole anisotropy and the motion of Earth, this term could
be subtracted. The remainder is then quadrupole anisotropy of purely cosmological
origin.
Since the precision of the COBE measurements surpassed all previous experiments
one can well understand that such small temperature variations had not been seen
before. The importance of this discovery was succinctly emphasized by the COBE
team who wrote that ‘a new branch of astronomy has commenced’. The story of the
COBE discoveries have been fascinatingly narrated by George Smoot [7].
8.3 Polarization
The perturbations to the baryon density and the radiation temperature in the tightly
coupled baryon–photon fluid are scalar, thus corresponding to a monopole moment
(퓁=0). As we saw previously, the radiation field also exhibits dipole perturbations
(퓁=1) which are coupled to the baryon bulk velocity, but there are no vector or tensor
perturbations. Tensor perturbations would be due to gravitational waves, which have
only recently been claimed to have been observed by the BICEP2 Collaboration [8].
The quadrupole moment possessed by free-streaming photons couples more
strongly to the bulk velocity (the peculiar velocities) of the baryon–photon fluid than
to the density. Therefore, the photon density fluctuations generate temperature fluc-
tuations, while the velocity gradient generates polarization fluctuations.
Thomson Scattering. In Section 6.3 we briefly introduced elastic scattering of pho-
tons from free electrons, Equation (6.30), calledThomson scattering, or Compton scat-
tering, as it is called for higher frequencies. On thet occasion we ignored the fate of
the primordial photons, noting only that they were thermalized by this process before
decoupling. We also noted that unpolarized photons are polarized by the anisotropic
Thomson scattering process, but as long as the photons continued to meet free elec-
trons their polarization was washed out, and no net polarization was produced. At
a photon’s last scattering, however, the induced polarization remains and the subse-
quently free-streaming photon possesses a quadrupole moment (퓁=2).
Consider a plane wave of monochromatic light with frequency휈moving along the
momentum vector in the푧direction (cf. Figure 8.4). The components of the wave’s
electric field vectorEin the (푥,푦)-plane oscillate with time푡in such a way that they
can be written
퐸푥(푡)=푎푥(푡)cos[휈푡−휃푥(푡)],퐸푦(푡)=푎푦(푡)cos[휈푡−휃푦(푡)], (8.25)where푎푥(푡)and푎푦(푡)are the amplitudes, and휃푥(푡)and휃푦(푡)are the phase angles.