Brief Review on Scalar Field Dark Matter Models

The existence of dark matter in the universe has been solidly established in the last decades, after the arrival of accurate cosmological and astrophysical observations, and some consider it the most challenging problem in modern physics. Given the magnitude of the problem, one cannot discard the existence of new particles with properties that may look exotic in comparison with our current understanding of ordinary matter. This is the case for the so-called scalar field dark matter model, which assumes the existence of a (probably fundamental) scalar field with a very tiny mass that can have observable consequences in the formation of cosmological structure. We present here a brief account of the main properties of an ultra-light scalar field (with masses of the order of 10(-22) eV/c(2)) and how different observations have been used in the last two decades to put constraints on its physical parameters. Among other topics, we review the cosmological solutions of the model, discuss the features of its self-gravitating equilibrium configurations, revisit the gravitational collapse for the formation of galaxies, and revise the possibility to find a soliton structure in the center of dark matter halos.