The Euclid mission, a European Space Agency-led mission launched in July 2023, is set to transform our understanding of the Universe by exploring its most elusive constituents: dark energy and dark matter. Together, they account for 95% of the cosmos, dictating its structure, evolution, and eventual fate. Euclid is currently surveying one-third of the sky to construct the most extensive 3D map of the Universe ever created. By using deep imaging and spectroscopic data, it traces the distribution of galaxies and the subtle distortions caused by gravitational lensing with unparalleled precision.
By connecting theory with observations, Euclid aims to uncover the properties of dark energy driving cosmic acceleration and the distribution of dark matter shaping large-scale cosmic structures. At the heart of this endeavor lies the challenge of cosmological statistical inference: extracting robust conclusions about the nature of dark energy and dark matter from vast, complex datasets. This talk will explore how cutting-edge statistical techniques and powerful computational tools, including Python-based analysis pipelines, are being used to compare theoretical models against Euclid's observations. We will discuss the role of Bayesian inference, machine learning, and advanced simulations in constraining cosmological parameters and testing extensions to the standard model of cosmology.