  We investigate two-field inflationary models in which scalar cosmological
pertubations are generated via a spectator field nonminimally coupled to
gravity, with the particular emphasis on curvaton scenarios. The principal
advantage of these models is in the possibility to tune the spectator spectral
index via the nonminimal coupling. Our models naturally yield red spectrum of
the adiabatic perturbation demanded by observations. We study how the
nonminimal coupling affects the spectrum of the curvature perturbation
generated in the curvaton scenarios. In particular we find that for small,
negative nonminimal couplings the spectral index gets a contribution that is
negative and linear in the nonminimal coupling. Since in this way the curvature
spectrum becomes redder, some of curvaton scenarios can be saved, which would
otherwise be ruled out. In the power law inflation we find that a large
nonminimal coupling is excluded since it gives the principal slow roll
parameter that is of the order of unity. Finally, we point out that nonminimal
coupling can affect the postinflationary growth of the spectator perturbation,
and in this way the effectiveness of the curvaton mechanism.
