The most interesting features of CMB lies in the presence of temperature fluctuations as they are most closely related to the density fluctuations that existed at this epoch.
In addition, one can also observe the polarization of the CMB. Although one needs in principle three Stokes parameters to describe polarization (Q and U for linear polarization and V for circular polarization), almost all models predict that only linear polarization can be produced in the early universe. Moreover, the Q and U Stokes parameters are not very interesting because they explicitely depend on the choice of the coordinate axes, so that it is more convenient to use two other related parameters, usually called the "electric" and "magnetic" part of the polarization and noted E and B. These parameters are computed using linear but nonlocal combination (i.e., involving derivatives) of the two Stokes parameters Q and U and are invariant under rotation of the coordinate axes.
The cosmological information is therefore extracted from the three temperature (T), E, and B maps. At present, most studies focus on the analysis of the two point correlation function in these maps. The reason for this is twofold:
First, a large class of models predict that observed fluctuations are Gaussian, so that the only relevant information in the maps are in their two-point correlation functions.
Second, it is much easier to extract the two-point correlation function that higher order statistics from the maps, especially when the signal-to-noise ratio is not very good.
Finally, one can also study the cross correlation between these maps. One can show that for symmetry reasons, the only non zero cross-correlation is between the T and E maps.
One therefore has four observable correlation functions, which are conveniently named TT, TE, EE and BB. For convenience, one prefers to study the corresponding power spectra, i.e., one decomposes the angular correlation function into Legendre polynomial and the information is then encoded into the coefficients of the Legendre polynomial, the so-called Cl.
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