Understanding the reionization of the intergalactic medium (IGM) by the first luminous sources remains an important open problem in cosmology. During Reionization ionization fronts propagate through the IGM, heating the reionized gas. This heat injection can be observed over a redshift interval of ∆z ∼ 1 due to the long cooling times in the low-density IGM. Simultaneously, the mean free path of ionizing photons (λmfp) describing the ultraviolet background (UVB) rapidly evolves as bubbles of reionized gas, where the UVB is stronger, merge. Thus, constraining the thermal state of the IGM and the evolution of λmfp can, in turn, be used to constrain reionization. Transmission in the Lyman-α (Lyα) forest, the ubiquitous Lyα absorption lines produced by residual neutral hydrogen in the IGM along quasar sightlines, offers a powerful tool to investigate these phenomena.

Here I present studies that look into utilizing the z > 5 Lyα forest to constrain Reionization via the thermal state of the IGM and λmfp. First, I use wavelet analysis as an initial clustering statistic and shows improvement on simulated temperature constraints when compared to measurements from the 1D Lyα forest power spectrum. This work also notes the importance of careful accounting of the correlations between datasets to ensure observational constraints are not over-confident. The next two studies use the Lyα forest auto-correlation function at z ≥ 5.4 as the clustering statistic. The second study demonstrates the potential in constraining λmfp from simulated data while the third does the same for the temperature. Both of these do careful statistical inference tests to ensure the results are not over-confident and describe a method to guarantee statistical robustness of measurements. The final study makes measurements of the Lyα forest auto-correlation functions at z > 5 from the XQR-30 data set. Preliminary comparisons of these measurements to the models from the second study are done, showing agreement with previous measurements of λmfp. Each of these contribute to our understanding of the high-z Lyα forest and how it can be used to constrain Reionization.