Euclid: Testing the Copernican principle with next-generation surveys

Context. The Copernican principle, the notion that we are not at a special location in the Universe, is one of the cornerstones of modern cosmology. Its violation would invalidate the Friedmann-Lemaître-Robertson-Walker metric, causing a major change in our understanding of the Universe. Thus, it is of fundamental importance to perform observational tests of this principle. Aims. We determine the precision with which future surveys will be able to test the Copernican principle and their ability to detect any possible violations. Methods. We forecast constraints on the inhomogeneous Lemaître-Tolman-Bondi (LTB) model with a cosmological constant Λ, basically a cosmological constant Λ and cold dark matter (CDM) model but endowed with a spherical inhomogeneity. We consider combinations of currently available data and simulated Euclid data, together with external data products, based on both Λ CDM and Λ LTB fiducial models. These constraints are compared to the expectations from the Copernican principle. Results. When considering the Λ CDM fiducial model, we find that Euclid data, in combination with other current and forthcoming surveys, will improve the constraints on the Copernican principle by about 30%, with ±10% variations depending on the observables and scales considered. On the other hand, when considering a Λ LTB fiducial model, we find that future Euclid data, combined with other current and forthcoming datasets, will be able to detect gigaparsec-scale inhomogeneities of contrast -0.1. Conclusions. Next-generation surveys, such as Euclid, will thoroughly test homogeneity at large scales, tightening the constraints on possible violations of the Copernican principle.