The Lya forest: the interplay between large-scale structure evolution
and small-scale baryonic physics

Neutral hydrogen in the Intergalactic Medium produces a collection of
Ly$\alpha$ absorbtions, called the Ly$\alpha$ forest, seen in the
spectra of background objects. According to the common paradigm, neutral
hydrogen in the IGM evolves from primordial density fluctuations in a
low density and photo-ionized environment. It therefore acts as a direct
tracer of Dark Matter (DM). However, it also implies that temperature
and density are thightly coupled, giving rise to degeneracies between
parameters describing either cosmology or the IGM thermal history. The
Ly$\alpha$ forest 1D power spectrum is sensitive to clustering on small
scales, and as such to the smoothing scale of relativistic particles. It
has been used to put the strongest constraints on the sum of the
neutrino masses and to study DM models. To infer cosmological
constraints and to test our models at the percent level accuracy, the
measurements need to be compared to state-of-the-art hydrodynamical
simulations. We also need to refine our understanding of the impact of
galactic feedbacks on the IGM temperature.

I will present the analysis that leads to the most recent P1D
measurement. As the current uncertainties are at the percent level, and
will even shrink further in the DESI era, the P1D becomes sensitive to
complex mechanical effects known as AGN feedback. We use Adaptative Mesh
Refinement (AMR) hydrodynamical simulations, the Horizon-AGN and
Horizon-noAGN simulations, to evaluate its impact on the P1D and prevent
degeneracies with neutrino effects. Finally I will present the most
up-to-date constraints on the mass of active neutrinos and on Warm Dark
Matter models.