Euclid: Forecast constraints on consistency tests of the $\Lambda$CDM
  model
  The standard cosmological model is based on the fundamental assumptions of a
spatially homogeneous and isotropic universe on large scales. An observational
detection of a violation of these assumptions at any redshift would immediately
indicate the presence of new physics. We quantify the ability of the Euclid
mission, together with contemporary surveys, to improve the current sensitivity
of null tests of the canonical cosmological constant $\Lambda$ and the cold
dark matter (LCDM) model in the redshift range $0<z<1.8$. We considered both
currently available data and simulated Euclid and external data products based
on a LCDM fiducial model, an evolving dark energy model assuming the
Chevallier-Polarski-Linder (CPL) parameterization or an inhomogeneous
Lema\^{\i}tre-Tolman-Bondi model with a cosmological constant $\Lambda$ (LLTB),
and carried out two separate but complementary analyses: a machine learning
reconstruction of the null tests based on genetic algorithms, and a
theory-agnostic parametric approach based on Taylor expansion and binning of
the data, in order to avoid assumptions about any particular model. We find
that in combination with external probes, Euclid can improve current
constraints on null tests of the LCDM by approximately a factor of three when
using the machine learning approach and by a further factor of two in the case
of the parametric approach. However, we also find that in certain cases, the
parametric approach may be biased against or missing some features of models
far from LCDM. Our analysis highlights the importance of synergies between
Euclid and other surveys. These synergies are crucial for providing tighter
constraints over an extended redshift range for a plethora of different
consistency tests of some of the main assumptions of the current cosmological
paradigm.
