Information Gains from Cosmological Probes
  In light of the growing number of cosmological observations, it is important
to develop versatile tools to quantify the constraining power and consistency
of cosmological probes. Originally motivated from information theory, we use
the relative entropy to compute the information gained by Bayesian updates in
units of bits. This measure quantifies both the improvement in precision and
the 'surprise', i.e. the tension arising from shifts in central values. Our
starting point is a WMAP9 prior which we update with observations of the
distance ladder, supernovae (SNe), baryon acoustic oscillations (BAO), and weak
lensing as well as the 2015 Planck release. We consider the parameters of the
flat $\Lambda$CDM concordance model and some of its extensions which include
curvature and Dark Energy equation of state parameter $w$. We find that,
relative to WMAP9 and within these model spaces, the probes that have provided
the greatest gains are Planck (10 bits), followed by BAO surveys (5.1 bits) and
SNe experiments (3.1 bits). The other cosmological probes, including weak
lensing (1.7 bits) and {$\rm H_0$} measures (1.7 bits), have contributed
information but at a lower level. Furthermore, we do not find any significant
surprise when updating the constraints of WMAP9 with any of the other
experiments, meaning that they are consistent with WMAP9. However, when we
choose Planck15 as the prior, we find that, accounting for the full
multi-dimensionality of the parameter space, the weak lensing measurements of
CFHTLenS produce a large surprise of 4.4 bits which is statistically
significant at the 8 $\sigma$ level. We discuss how the relative entropy
provides a versatile and robust framework to compare cosmological probes in the
context of current and future surveys.
