Information Gains from Cosmic Microwave Background Experiments
  To shed light on the fundamental problems posed by Dark Energy and Dark
Matter, a large number of experiments have been performed and combined to
constrain cosmological models. We propose a novel way of quantifying the
information gained by updates on the parameter constraints from a series of
experiments which can either complement earlier measurements or replace them.
For this purpose, we use the Kullback-Leibler divergence or relative entropy
from information theory to measure differences in the posterior distributions
in model parameter space from a pair of experiments. We apply this formalism to
a historical series of Cosmic Microwave Background experiments ranging from
Boomerang to WMAP, SPT, and Planck. Considering different combinations of these
experiments, we thus estimate the information gain in units of bits and
distinguish contributions from the reduction of statistical errors and the
`surprise' corresponding to a significant shift of the parameters' central
values. For this experiment series, we find individual relative entropy gains
ranging from about 1 to 30 bits. In some cases, e.g. when comparing WMAP and
Planck results, we find that the gains are dominated by the surprise rather
than by improvements in statistical precision. We discuss how this technique
provides a useful tool for both quantifying the constraining power of data from
cosmological probes and detecting the tensions between experiments.
