A scalar field modelling of the rotational curves of spiral galaxies

In a previous work \cite{mbeleka}, we have modelled the rotation curves (RC) of spiral galaxies by including in the equation of motion dynamical terms from an external real self-interacting scalar field, $\varphi$, minimally coupled to gravity and which respects the equivalence principle in the absence of electromagnetic fields. This model appears to have three free parameters : the turnover radius, $r_0$, the maximum rotational velocity, $v_{max} = v(r_{0})$,plusastrictlypositiveinteger,$n$\mathrm{.}Here,thecouplingofthe$\phi$-field to other kinds of matter is emphasized at the expense of its self-interaction. This reformulation presents the very advantageous possibility that the same potential may be used now for all galaxies. New correlations are established.