The fundamental physical properties of Dark Matter (DM) e.g. particle mass, spin, couplings, etc. still remain a mystery. If DM particles are spinless and ultra-light (m~10-22 eV), what are the observational constraints on its properties like mass and in particular, self-couplings? In this talk we attempt to answer this question by considering the following scenarios: (a) Using observational upper limits on the amount of mass contained within some region around the galactic centre, one can impose constraints in the λ-m plane, where allowed self-couplings can be as small as λ~±10-96, (b) requiring that observed galactic rotation curves of dwarf galaxies as well as an empirical soliton-halo relation have to be simultaneously satisfied allows one to probe self-couplings as small as λ~𝒪(10-90), and (c) survival of dwarf satellite galaxies orbiting in the potential of larger halos on cosmological timescales can be used to probe both attractive and repulsive self-couplings as small as λ~±10-92. Towards the end of the talk, we shall also discuss how machine learning models like neural networks could be used to learn DM parameters (in particular ULDM mass m) from galactic rotation curves.
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