Galaxy Evolution and Large Scale Structure with HI: paving the way to 21cm line and Lyman-alpha forest upcoming surveys

The neutral atomic hydrogen (HI) is ubiquitous in the universe. In this thesis work, I analyze its role in the fields of galaxy evolution and large scale structure, within the context of modern state-of-the-art HI redshift surveys. In the first part of the work -- dedicated to galaxy evolution with HI -- I investigate the correlation between the amount of HI in galaxies and several different internal and external galaxy properties. I first test the impact of typical variables involved in the stacking procedure (primary beam correction, weighting scheme, redshift uncertainties, and noise) using realistic simulated MeerKAT datacubes at $0.005<z<0.084$, covering an area of $\sim 6$ deg$^2$. Then, I perform an analysis of the correlations between the HI amount and internal properties (stellar mass $M_*$, SFR, and sSFR) of galaxies beyond the Local universe in the COSMOS field. In particular, I stack HI-undetected spectra of $9023$ star-forming galaxies at $0.23<z<0.49$ (median redshift $z\sim 0.37$) using HI emission data from the MIGHTEE survey, acquired with the MeerKAT telescope. I report the first detection of HI scaling relations beyond the nearby universe. Subsequently, I study possible correlations between HI in galaxies and the surrounding large-scale structure environment. I adopt again a HI spectral stacking approach, using the same setup as the previous study. I find that the cosmic web type is the large-scale structure parameter which correlates most with the amount of HI in galaxies. Additionally -- as a separate project -- I investigate the dependence of the baryonic Tully-Fisher relation at $z\sim 0$ on the role of each galaxy as central/satellite inside its host dark matter halo, using a catalog built by cross-matching the ALFALFA-SDSS public catalog and the most recent SDSS galaxy group catalog. In the second part of this dissertation -- dedicated to cosmology and large-scale structure with HI -- I study and develop effective field-level bias models to describe the spatial distribution and clustering of HI on cosmological scales. In particular, I focus in this thesis on the Lyman-alpha forest. I start by studying the nature of the bias relations linking different baryon fields (ionized gas density HII, HI, and IGM temperature) at z=2. In particular, I find that a natural hierarchy of such relations exists, and that nonlocal terms have an important impact on the predictions. I then demonstrate that once the HII and HI fields are obtained, the Lyman-alpha forest can be predicted by mapping it onto the HII and HI fields. Subsequently, I implement in an analytical framework the findings from the studies described above to improve the Fluctuating Gunn-Peterson Approximation (FGPA), widely-used in the last decades to model the Lyman-alpha forest in a quick manner, making it sensitive to nonlocal dependencies. Finally, I employ two fixed-and-paired cosmological hydrodynamic simulations to investigate the Lyman-alpha forest BAO. In particular, I find tentative evidence for a $\sim 2.2\%$ positive shift of the BAO peak in redshift space, alleviating the existing known tension with the $\Lambda$CDM model.