Euclid: Forecast constraints on the cosmic distance duality relation
  with complementary external probes
  In metric theories of gravity with photon number conservation, the luminosity
and angular diameter distances are related via the Etherington relation, also
known as the distance-duality relation (DDR). A violation of this relation
would rule out the standard cosmological paradigm and point at the presence of
new physics. We quantify the ability of Euclid, in combination with
contemporary surveys, to improve the current constraints on deviations from the
DDR in the redshift range $0<z<1.6$. We start by an analysis of the latest
available data, improving previously reported constraints by a factor of 2.5.
We then present a detailed analysis of simulated Euclid and external data
products, using both standard parametric methods (relying on phenomenological
descriptions of possible DDR violations) and a machine learning reconstruction
using Genetic Algorithms. We find that for parametric methods Euclid can (in
combination with external probes) improve current constraints by approximately
a factor of six, while for non-parametric methods Euclid can improve current
constraints by a factor of three. Our results highlight the importance of
surveys like Euclid in accurately testing the pillars of the current
cosmological paradigm and constraining physics beyond the standard cosmological
model.
