Abstract
The process of structure formation in the Universe can be explained by means of the gravitational instability of the different matter components, in particular that of the so-called dark matter field. In this work, we consider that dark matter can be described by an ultra-light scalar field minimally coupled to gravity, and its gravitational instability in an expanding universe is studied with the help of standard techniques for fluid matter components. Analytical and numerical solutions are shown, for both linear and non-linear perturbations, and compared with those of the standard cold dark matter model. We conclude that non-linear perturbations of the scalar field are indistinguishable from those of cold dark matter as long as the field mass is larger than 10−25eV.
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