Scalar Field Dark Matter, Cross Section and Planck-Scale Physics

In recent papers we have proposed that the dark matter of the Universe could be from scalar field origin. In this letter, we find that if the scale of renormalization of the model is of order of the Planck Mass, then a scalar field $\Phi $ endowed with the scalar potential $V=V_{o}[\cosh {(\lambda \sqrt{\kappa_{0}}\Phi)}-1] can be a reliable model for dark matter in galaxies. The predicted scattering cross section fits the value required for self-interacting dark matter and the additional degree of freedom of the theory is of order of hundreds of TeV.