Abstract: The Dark Energy Spectroscopic Instrument (DESI) collaboration is conducting a 5 year redshift survey of 40 million extra-galactic sources over 14,000 square degrees of the northern sky. One of its primary goals is to measure the cosmic expansion history with baryon acoustic oscillations (BAO). I will present the measurement of BAO in galaxy, quasar and Lyman-alpha forest tracers from the first year of observation. With 5.7 million galaxy and quasar redshifts in the range 0.1 < z < 2.1, and 420,000 Lyman-alpha forest quasars at higher redshift, the aggregate precision on BAO is of 0.52% at z<2.1 and 1.1% at an effective redshift z=2.3, surpassing in a year two decades of observations with the SDSS. I will present some of the numerous validation tests performed with simulations and blinded data. I will then highlight the main cosmological results, with improved constraints on the dark energy equation of state, the Hubble parameter, spatial curvature, and the sum of neutrino masses.
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