Fundamental physics with the cosmic web

I will review the physics of the intergalactic medium, i.e. the low-density cosmic web connecting galaxies. I will show that this physics is simple and allows us to address structure formation processes and fundamental physics at scales and redshifts not probed by other observables (like galaxies and the cosmic microwave background). Among the different questions that we can ask I will focus on: the nature of dark matter, neutrino masses and primordial magnetic fields. In order to obtain constraints we will rely on a large set of hydrodynamical simulations and high redshift spectroscopic data of the Lyman-alpha forest, which is the main manifestation of the cosmic web.