Determining the mass of cosmological neutrinos using Lyman-alpha forests

In the work presented in this thesis, I use the power spectrum of the transmitted flux in the Lyman-alpha (Ly-$alpha$) forest of distant quasars to constrain the mass of cosmological neutrinos in the context of four seperate projects. Neutrinos leave a signature imprint on large scale structures in the Universe through their free-streaming, which manifests as a deficit of matter density fluctuations on typical length scales that are inversely proportional to their rest mass. This typical free-streeming scale, of order a few Mpc, can be probed by Ly-$alpha$ forests which are imprints of the neutral atomic Hydrogen density along the background quasar's line-of-sight. I use the Ly-$alpha$ flux power spectrum from mainly two large scale structure surveys: the $13,821$ low-resolution quasar spectra from the ninth data release of SDSS (BOSS) in 12 redshift bins from $langle z rangle = 2.2$ to $4.4$; and the $100$ high-resolution quasar spectra from the XQ-100 survey (of the VLT's XShooter spectrograph) in 3 redshift bins, $langle z rangle = 3.20, 3.56$ and $3.93$. This enables us to probe scales from $k geqslant 0.001~s/mathrm{km}$ to $k leqslant 0.02$ and $k leqslant 0.07~ s/mathrm{km}$ respectively.Modeling the flux power spectrum requires solving the non-linear regime of structure formation and the intergalactic gas in the cosmological hydrodynamics simulations that are used to that effect. I controlled for several of many systematic uncertainties related to the simulations. First, I ran simulations with different initial conditions to quantify the sampling variance. I then tested the accuracy of a splicing technique that we use to construct the flux power spectrum from lower size and lower resolution simulations. This required producing a complete run of a $(100~h^{-1}mathrm{Mpc})^3$ comoving cube containing $2 times 2048^3$ dark matter particles and baryons. This enabled our working group to enhance the previously established constraints on the sum of neutrino masses from $sum m_nu < 0.15~mathrm{eV}$ to the most stringent constraint to date $sum m_nu < 0.12~mathrm{eV}$ with $95%$ confidence. I then worked on implementing right-handed neutrinos in non-cold dark matter cosmological frameworks. A substancial amount of work has gone into applying plausible initial conditions that would accurately model the free-streaming effect of these types of particles. I put the most stringest constraints (at the time of publication) on the mass of non-resonantly produced sterile neutrinos as pure warm dark matter candidates, $m_nu lesssim 25~mathrm{keV}$ at $95%$ confidence. I extended this investigation into a mixed warm plus cold dark matter cosmology. Finally, I implement right-handed neutrinos produced in presence of a lepton asymmetry which boosts their production and lowers their free-streaming scale. I started a collaboration with a team of theoretical physicists involved in searching for astrophysical evidence for the existance of such resonantly-produced right-handed neutrinos in dark matter rich systems. Our new-born collaboration has enabled the first ever constraints on their mass using the Ly-$alpha$ forest power spectrum.