<i>Colloquium</i> : The cosmic dipole anomaly

The cosmological principle, which states that the Universe must be statistically isotropic and homogeneous on large scales, is a foundational principle of the standard model of cosmology, known as lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}$CDM). The validity of this principle can be tested by assessing the compatibility of a dipole anisotropy in the large-scale distribution of matter with the dipole observed in the cosmic microwave background, interpreted in the $\mathrm{\ensuremath{\Lambda}}$CDM model as due to our local peculiar motion. This Colloquium describes the methodology for such a test and presents its outcome based on the analysis of recent large catalogs of radio galaxies and quasars, revealing a significant inconsistency between the two dipoles. The authors review these recent findings, as well as potential biases, systematic issues, and alternate interpretations, and discuss how this anomaly could challenge the standard description of our Universe based on the $\mathrm{\ensuremath{\Lambda}}$CDM model.