The information content of cosmic microwave background anisotropies

TL;DR

This paper evaluates the maximum information extractable from CMB anisotropies under sample variance limits, highlighting the roles of polarization modes and lensing in constraining cosmological parameters.

Contribution

It provides a pedagogical analysis of the information content in CMB data, emphasizing the impact of polarization and lensing on parameter constraints without relying on specific experimental forecasts.

Findings

Adding E-mode polarization doubles the available modes.

Inclusion of B-mode polarization and lensing enhances information content.

CMB data can constrain neutrino mass beyond current limits.

Abstract

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.