  With the high-precision data from current and upcoming experiments, it
becomes increasingly important to perform consistency tests of the standard
cosmological model. In this work, we focus on consistency measures between
different data sets and methods that allow us to assess the goodness of fit of
different models. We address both of these questions using the relative entropy
or Kullback-Leibler (KL) divergence [Kullback et al., 1951]. First, we revisit
the relative entropy as a consistency measure between data sets and further
investigate some of its key properties, such as asymmetry and path dependence.
We then introduce a novel model rejection framework, which is based on the
relative entropy and the posterior predictive distribution. We validate the
method on several toy models and apply it to Type Ia supernovae data from the
JLA and CMB constraints from Planck 2015, testing the consistency of the data
with six different cosmological models.
