  In this paper we consider $\phi^2$ scalar field potential as a candidate to
dark matter. If it is an ultralight boson particle, it condensates like a
Bose-Einstein system at very early times and forms the basic structure of the
Universe. Real scalar fields collapse in equilibrium configurations that
oscillate in space-time (oscillatons).The cosmological behavior of the field
equations are solved using the dynamical system formalism. We use the current
cosmological parameters as constraints for the present value of the scalar
field. We reproduce the cosmological predictions of the standard $\Lambda$CDM
model with this model. Therefore, scalar field dark matter seems to be a good
alternative to cold dark matter nature.
