Cosmology beyond BAO from the 3D distribution of the Lyman-α forest measured by DESI

The Lyman-α (Lyα) forest is currently one of the most powerful probes of large-scale structure (LSS) at high redshift (z > 2). The Dark Energy Spectroscopic Instrument (DESI) is in the process of observing about one million forests, giving us unprecedented access to the distribution of neutral hydrogen in the high redshift Universe. While previous surveys have focused on measuring baryon acoustic oscillations (BAO) from this 3D distribution, we are now working towards extracting more information (beyond BAO) with DESI. In this talk I will show how we can use the full shape of the Lyα forest auto-correlation and its cross-correlation with quasars to improve constraints on the cosmic expansion rate through the Alcock-Paczynski (AP) effect, and measure the linear growth rate of structure from redshift space distortions (RSD). We have recently used extended Baryon Oscillation Spectroscopic Survey (eBOSS) data to measure the AP effect from the full shapes of Lyα correlations and found that it provides a factor of two tighter constraints compared to BAO analyses. Finally, I will show forecasts of Lyα forest full-shape measurements from DESI.