Beyond ΛCDM with DESI: Full-Shape Constraints on Gravity and Cosmological Tensions

The Dark Energy Spectroscopic Instrument (DESI) presents an unprecedented view of large-scale structure, enabling percent-level measurements of galaxy clustering across a wide redshift range. While the DESI DR2 baryon acoustic oscillation (BAO) results have been published earlier this year, the forthcoming full-shape analysis will extend these measurements by exploiting additional information sensitive to the growth of structure and the nature of gravity on large scales. This talk will begin with a brief introduction to full-shape clustering measurements, followed by an overview of key methodological and modeling updates implemented between DESI Year 1 and Year 2. I will further present the efforts aimed at testing physics beyond ΛCDM, with a particular emphasis on modified gravity models. The enhanced sensitivity of full-shape measurements to potential deviations from General Relativity will be discussed, alongside current and planned analyses exploring these signatures. These efforts will then be placed within the broader context of ongoing cosmological tensions, emphasising the potential of DESI full-shape data to distinguish between new physics and systematic effects.