In this paper, we consider φ2 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 which oscillate in space–time (oscillatons).The cosmological behaviour 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 and reproduce the cosmological predictions of the standard Λ cold dark matter model with this model. Therefore, scalar field dark matter seems to be a good alternative to cold dark matter nature.

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a Randall-Sundrum brane. The simplest kinds of self-interaction potentials are investigated: a) constant potential, and b) exponential potential. It is shown that the dynamics of the Randall-Sundrum model significantly differs from the standard four-dimensional behavior at early times: in all cases of interest the (singular) empty universe is the past attractor for every trajectory in phase space, meanwhile the kinetic energy-dominated solution is always a saddle critical point. The late-time dynamics is not affected by the brane effects.

In this work we study several scalar field potentials as a plausible candidate to be the dark matter in the universe. The main idea is the following; if the scalar field 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 which oscillate in spacetime (oscillatons). The cosmological behavior of the field equations are solved using the dynamical system formalism. We use the currentcosmologicalparameters as constraints for the free parameters of the scalar field potentials. We are able to reproduce very well the cosmological predictions of the standard ACDM model with some scalar field potentials. Therefore, scalar field dark matter seems to be a good alternative to be the nature of the dark matter of the universe.