The information content of cosmic microwave background anisotropies
  The cosmic microwave background (CMB) contains perturbations that are close
to Gaussian and isotropic. This means that its information content, in the
sense of the ability to constrain cosmological models, is closely related to
the number of modes probed in CMB power spectra. Rather than making forecasts
for specific experimental setups, here we take a more pedagogical approach and
ask how much information we can extract from the CMB if we are only limited by
sample variance. We show that, compared with temperature measurements, the
addition of E-mode polarization doubles the number of modes available out to a
fixed maximum multipole, provided that all of the TT, TE, and EE power spectra
are measured. However, the situation in terms of constraints on particular
parameters is more complicated, as we explain and illustrate graphically. We
also discuss the enhancements in information that can come from adding B-mode
polarization and gravitational lensing. We show how well one could ever
determine the basic cosmological parameters from CMB data compared with what
has been achieved with Planck, which has already probed a substantial fraction
of the TT information. Lastly, we look at constraints on neutrino mass as a
specific example of how lensing information improves future prospects beyond
the current 6-parameter model.
