  In this paper, we prove an optimal inequality between the potential function
of a complete Schouten soliton and the norm of its gradient. We also prove that
these metrics have bounded scalar curvature of defined sign. As an application,
we prove that the potential function of a Shrinking Schouten soliton grows
linearly and provide optimal estimates for the growth of the volume of geodesic
balls, without any further assumption.
