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We study the viability of a complex scalar field $\chi$ with self-interactingpotential $ V = m^\chi_0/2 \, |\chi|^2 + h \, |\chi|^4$ as dark matter. Thescalar field is produced at reheating through the decay of the inflaton fieldand then, due to the self-interaction, a Bose-Einstein condensate of $\chi$particles forms. The condensate represents dark matter in that model. Weanalyze the cosmological evolution of the model, stressing how, due to thepresence of the self-interaction, the model naturally admits dark matterdomination at late times, thus avoiding any fine tuning on the energy densityof the scalar field at early times. Finally we give a lower bound for the sizeof dark matter halos at present time and we show that our model is compatiblewith dark matter halos greater than $0.1 \, Kpc$ and with BBN and CMB bounds onthe effective number of extra neutrinos $\Delta_\nu^{eff}$. Therefore, themodel is viable and for $h\simeq 10^{-4}-10^{-12}$ one obtains a mass $m^\chi\simeq m^{\chi}_0 \simeq 1-10^{-2} \, eV$ for dark matter particles fromradiation-matter equality epoch to present time, but at temperatures $T_\gamma\gg 10 \, eV$, where $T_\gamma$ is the photons temperature, thermal correctionsto $m^\chi_0$ due to the self-coupling $h$ are dominant.

Viability of complex self-interacting scalar field as dark matter