Determining the absolute neutrino mass scale and the neutrino mass hierarchy are central goals in particle physics, with important implications for the Standard Model. However, the final answer may come from cosmology, as laboratory experiments provide measurements for two of the squared mass differences and a stringent lower bound on the total neutrino mass -but the upper bound is still poorly constrained, even when considering forecasted results from future probes. Cosmological tracers are

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... y sensitive to neutrino properties and their total mass, because massive neutrinos produce a specific redshiftand scale-dependent signature in the power spectrum of the matter and galaxy distributions. Stringent upper limits on m ν will be essential for understanding the neutrino sector, and will nicely complement particle physics results. To this end, we describe here a series of cosmological hydrodynamical simulations which include massive neutrinos, specifically designed to meet the requirements of the Baryon Acoustic Spectroscopic Survey (BOSS) and focused on the Lyman-α (Lyα) forest -also a useful theoretical ground for upcoming surveys such as SDSS-IV/eBOSS and DESI. We then briefly highlight the remarkable constraining power of the Lyα forest in terms of the total neutrino mass, when combined with other state-of-the-art cosmological probes, leading to a stringent upper bound on m ν .