Viability of complex self-interacting scalar field as dark matter

We study the viability of a complex scalar field χ with self-interacting potential V=m0χ/2|χ|2+h|χ|4 as dark matter. The scalar field is produced at reheating through the decay of the inflaton field and then, due to the self-interaction, a Bose-Einstein condensate of χ particles forms. The condensate represents dark matter in that model. We analyze the cosmological evolution of the model, stressing how, due to the presence of the self-interaction, the model naturally admits dark matter domination at late times, thus avoiding any fine tuning on the energy density of the scalar field at early times. Finally we give a lower bound for the size of dark matter halos at present time and we show that our model is compatible with dark matter halos greater than 0.1 kpc and with BBN and CMB bounds on the effective number of extra neutrinos Δνeff. Therefore, the model is viable and for h≃10−4-10−12 one obtains a mass mχ≃m0χ≃1-10−2 eV for dark matter particles from radiation-matter equality epoch to present time, but at temperatures Tγ≫10 eV, where Tγ is the photons temperature, thermal corrections to m0χ due to the self-coupling h are dominant.