DESI is the first new generation galaxy survey to take data with the goal to shed light on the mechanism that drives the acceleration of the cosmic expansion. Is this accelerated expansion due to a mysterious dark energy component or is our theory of gravity based on General Relativity incomplete at very large scales?
Last November, the DESI collaboration published a new batch of papers that complements the one we published last April for the BAO analysis of the DESI Data Release 1. In this new analysis, we modelled and analysed the full broad-band shape of the galaxy two-point clustering to constrain not only the expansion history of the Universe as the BAO analysis does but also to constrain the formation of structures and the theory of gravity. In this seminar, I will briefly remind the DESI survey, then I will explain how we performed such a Full-Shape analysis of the DESI DR1 data and eventually I will present the cosmological results and implications regarding the nature of dark energy, neutrinos and gravity.