Different models of dark matter can be distinguished through the amount of free streaming they exhibit. A consequence of free streaming is the suppression of small-scale cosmic structure, which in...Show moreDifferent models of dark matter can be distinguished through the amount of free streaming they exhibit. A consequence of free streaming is the suppression of small-scale cosmic structure, which in turn could be detected through the Ly-α forest, a series of absorption features in quasar spectra. This thesis considers how peculiar velocities in the intergalactic medium, the gas that produces the absorption of the Ly-α forest, influence the flux power spectrum (FPS) of the Ly-α forest. We do this by calculating the FPS from high-resolution hydrodynamical simulations, performed using the SWIFT code, while taking into account peculiar velocities or ignoring them; it is shown that at large scales, peculiar velocities may introduce a Gaussian cutoff to the FPS. A model that relates the spatial scale corresponding to this cutoff to the density, thermal state and peculiar velocity dispersion of the intergalactic medium is proposed and tested at redshifts 4.0 ≤ z ≤ 6.0. It is found to be acceptable at 4.0 ≤ z ≤ 5.5, although only the average dependence on the peculiar velocity dispersion is correctly described; at z = 6.0, the proposed model can be rejected. The main venue for extending the research done here is thought to be the development of a model that describes the influence of peculiar velocities on smaller scales as well.Show less