Lambda-CDM model and small-scale-cosmology "crisis": from astrophysical explanations to new fundamental physics models

I review briefly three problems where tensions between predictions based on numerical simulations of the Lambda-CDM prototype and observations at small (galactic) scales occur. These include (i) the core-cusp problem on the galactic profiles, (ii) the missing satellite problem, and the (ii) too-big-to-fail problem. I explain what these problems are and present potential resolutions, first through some astrophysical mechanisms, which however, as I argue, fail to alleviate completely the problems, at least currently. Then, I discuss fundamental modifications of the Lambda-CDM model, through the inclusion of self-interacting dark matter (SIDM). I argue that a simple model of SIDM, with (warm) self-interacting right-handed neutrinos (RHN), that exist in minimal extensions of the Standard model of particle physics, appears promising in providing a resolution of the aforementioned "small-scale-Cosmology crisis", in particular the core-cusp problem, and an observationally consistent description of the core-halo structure in galaxies.