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WIMP Dark Matter and the First Stars: a critical overview

If Dark Matter (DM) is composed by Weakly Interacting Massive Particles, its annihilation in the halos harboring the earliest star formation episode may strongly influence the first generation of stars (Population III). Whereas DM annihilation at early stages of gas collapse does not dramatically affect the properties of the cloud, the formation of a hydrostatic object (protostar) and its evolution toward the main sequence may be delayed. This process involves DM concentrated in the center of the halo by gravitational drag, and no consensus is yet reached over whether this can push the initial mass of Population III to higher masses. DM can also be captured through scattering over the baryons in a dense object, onto or very close to the Main Sequence. This mechanism can affect formed stars and in principle prolonge their lifetimes. The strength of both mechanisms depends upon several environmental conditions and on DM parameters; such spread in the parameter space leads to very different scenarios for the observables in the Population. Here I summarize the state of the art in modelling and observational expectations, eventually highlighting the most critical assumptions and sources of uncertainty.