Simulating highly non-linear dark matter dynamics beyond LCDM

Most of the presently available data regarding the structure and the properties of the Universe are well described within the standard LCDM cosmological scenario. However, the underlying assumptions on which the standard framework is based on have been tested only over a restricted range of cosmic scales and cosmic epochs, and extremely severe fine-tuning problems still affect the rather peculiar choice of its parameters. Therefore, a wide range of extended cosmological models have been proposed in the literature to overcome these obstacles. Given the expected excellent high-precision data that will be available in the Precision Cosmology era, it will be possible to test such extensions of the standard cosmological model systematically, to constrain them or rule them out. This will require the theoretical predictions of observable quantities to achieve the same outstanding quality for many competing non-standard cosmologies. In order to obtain such accuracy over a wide range of scales and epochs, the use of large and complex numerical simulations will represent an essential tool. In this thesis, we present the research activity carried out during three years of Ph.D., focused on the implementation and application of alternative cosmological models beyond-LCDM in the cosmological hydrodynamical code P-Gadget3. In particular, our work concerned the development of refined numerical routines to perform and improve simulations of two classes of strongly and non-linearly interacting dark matter scenarios: Fuzzy Dark Matter and Growing Neutrino Quintessence models.