Structure formation with scalar field dark matter: the field approach

We study the formation of structure in the Universe assuming that dark matter can be described by a scalar field with a potential V(Φ) = −²²/2+λ⁴/4. We derive the evolution equations of the scalar field in the linear regime of perturbations. We investigate the symmetry breaking and possibly a phase transition of this scalar field in the early Universe. At low temperatures, the scalar perturbations have an oscillating growing mode and therefore, this kind of dark matter could lead to the formation of gravitational structures. In order to study the nonlinear regime, we use the spherical collapse model and show that, in the quadratic potential limit, this kind of dark matter can form virialized structures. The main difference with the traditional Cold Dark Matter paradigm is that the formation of structure in the scalar field model can occur at earlier times. Thus, if the dark matter behaves as a scalar field, large galaxies are expected to be formed already at high redshifts.