We use the large-scale distribution of matter in the universe to test our cosmological models. This is primarily done using baryon acoustic oscillations (BAO), which are measured in the two-point correlation function of this distribution. However, the entire matter field contains information at various scales, allowing us to better constrain our models than BAO alone. At redshifts greater than 2, the Lyman-alpha forest is the best probe of this matter distribution. The Lyman-alpha forest is a set of absorption lines measured in the spectra of distant sources. The large DESI spectroscopic survey has collected approximately one million of these spectra. Using the partial data set 'DR2,' we measured the BAO with an accuracy of 0.7%, which strongly constrains the expansion rate of the universe during the first billion years of its evolution.

This thesis aims to exploit the full set of large-scale Lyman-alpha data from DESI to obtain the strongest constraints on cosmological models possible. First, the student will apply a method known as reconstruction to improve the accuracy of BAO measurements by exploiting information from the matter density field. For the remainder of the thesis, the student will implement a new method known as simulation-based inference. Similar efforts have been carried out in our group with DESI galaxies. In this approach, the entire matter field is used directly to estimate cosmological parameters, particularly dark energy. Thus, the student will make an important contribution to DESI's final cosmological measurements with Lyman-alpha.

An internship is preferred before beginning this thesis.