Euclid preparation. 3-dimensional galaxy clustering in configuration space Part I: 2-point correlation function estimation

The two-point correlation function of the galaxy spatial distribution is a major cosmological observable that enables constraints on the dynamicsand geometry of the Universe. The Euclid mission aims at performing an extensive spectroscopic survey of approximately 20–30 million H-emitting galaxies up to about redshift two. This ambitious project seeks to elucidate the nature of dark energy by mapping the three-dimensionalclustering of galaxies over a significant portion of the sky. This paper presents the methodology and software developed for estimating the threedimensionaltwo-point correlation function within the Euclid Science Ground Segment. The software is designed to overcome the significantchallenges posed by the large and complex Euclid data set, which involves millions of galaxies. Key challenges include ecient pair counting,managing computational resources, and ensuring the accuracy of the correlation function estimation. The software leverages advanced algorithms,including kd-tree, octree, and linked-list data partitioning strategies, to optimise the pair-counting process. These methods are crucial forhandling the massive volume of data eciently. The implementation also includes parallel processing capabilities using shared-memory openmulti-processing to further enhance performance and reduce computation times. Extensive validation and performance testing of the software arepresented. Those have been performed by using various mock galaxy catalogues to ensure that it meets the stringent accuracy requirements of theEuclid mission. The results indicate that the software is robust and can reliably estimate the two-point correlation function, which is essential forderiving cosmological parameters with high precision. Furthermore, the paper discusses the expected performance of the software during differentstages of the Euclid Wide Survey observations and forecasts how the precision of the correlation function measurements will improve over themission’s timeline, highlighting the software’s capability to handle large data sets efficiently.Key words. large-scale structure of Universe - Cosmology: observations - Methods: statistical - Methods: data analysis