  We present maps classifying regions of the sky according to their information
gain potential as quantified by the Fisher information. These maps can guide
the optimal retrieval of relevant physical information with targeted
cosmological searches. Specifically, we calculate the response of observed
cosmic structures to perturbative changes in the cosmological model and chart
their respective contributions to the Fisher information. Our physical forward
modeling machinery transcends the limitations of contemporary analyses based on
statistical summaries to yield detailed characterizations of individual 3D
structures. We demonstrate this using galaxy counts data and showcase the
potential of our approach by studying the information gain of the Coma cluster.
We find that regions in the vicinity of the filaments and cluster core, where
mass accretion ensues from gravitational infall, are the most informative about
our physical model of structure formation in the Universe. Hence, collecting
data in those regions would be most optimal for testing our model predictions.
The results presented in this work are the first of their kind and elucidate
the inhomogeneous distribution of cosmological information in the Universe.
This study paves a new way forward to perform efficient targeted searches for
the fundamental physics of the Universe, where search strategies are
progressively refined with new cosmological data sets within an active learning
framework.
