Cosmology with Fuzzy Dark Matter

The standard ΛCDM model is successful in describing the large scale structure of the universe but has difficulties on small scales. As an alternative, the Fuzzy Dark Matter (FDM) model proposes that dark matter be composed of an ultralight scalar field with mass 10^-22 to 10^-21 eV. The dynamics of FDM is governed by the Schrodinger-Poisson equation which is very different from the CDM dynamics. In this talk, I will present the numerical simulations of FDM model with applications to the Lyman-alpha flux spectrum. Besides, the wave nature of FDM leads to the formation interference patterns and vortices. Such structures are absent in the CDM model and can have interesting observational consequences.