  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.
