Introduction to Scalar Field Dark Matter Structure Formation
Abril Suárez
Resumen
In this work we introduce a Φ^2 potential to describe the dynamics of our scalar field (SF) candidate to be the dark matter in the Universe, and as one of the main ingredients needed to obtain the large-scale structure we see today. We calculate and simulate some of the ingredients needed to obtain the matter density profile of the large-scale structure we observe now a days in a qualitative way. We begin assuming that the seeds of the early universe were small fluctuations that lived inside an homogeneous Friedmann- Lemaitre-Robertson-Walker (FLRW) background, and which are studied using the Linear Perturbation Theory, these fluctuations then grew because of gravitational instability, this way giving birth to what we see today: galaxies, clusters of galaxies, etc. We then work with the most general perturbed metric for scalar perturbations, which we use to obtain the homogeneous and perturbed Einstein’s equations together with the help of General Relativity. In calculating the energy density we used the conservation of the energy-momentum tensor, which is now also perturbed, and that together with the Einstein’s equations and the perturbed Klein-Gordon equation gave us our complete set of equations to be solved.
