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

Information Gains from Cosmic Microwave Background Experiments