The Lyman-alpha forest and small-scales applications
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The Lyman-$\alpha$ forest can be observed from the ground in the optical spectra of distant quasars at high redshifts ($z>2$). The Lyman-$\alpha$ forest consists of a series of Lyman-$\alpha$~absorption lines caused by intervening neutral hydrogen at various redshifts between the quasar and the observer. This is a powerful probe of the underlying matter density field at redshifts $z > 2$, as well as the astrophysical state of the intergalactic medium. More particularly, the small-scale distribution of neutral hydrogen ($\sim$ Mpc) is imprinted in the fluctuations of the Lyman-$\alpha$ forest along the line-of-sight, which can be accessed by measuring the one-dimensional Lyman-$\alpha$ forest power spectrum. In this talk, I will give a broad overview of the Lyman-$\alpha$ forest and its potential applications. I will give a concrete example of application with the measurement of the one-dimensional power spectrum on the first data release of the Dark Energy Spectroscopic Instrument (DESI) (Ravoux et al. 2025, Kara{\c c}ayl{\i} et al. 2025). A comparison of this measurement with theoretical predictions from hydrodynamical simulations was recently performed to constrain the amplitude and slope of the primordial power spectrum ($A_s$, $n_s$) and the sum of neutrino masses ($\sum m_{\nu}$) (Chaves-Montero et al. 2026). Future datasets and simulations will allow us to enhance these constraints and extend them to dark matter properties.