  We derive the semiclassical evolution of massless conformally coupled scalar
matter in the de Sitter space-time from the Born-Oppenheimer reduction of the
Wheeler-DeWitt equation. We find a remarkable difference with respect to the
minimally coupled case: the effect of the quantum gravitational corrections do
not depend on the momentum of the scalar mode up to second order in the Planck
length and, therefore, there are no relevant corrections to the dispersion
relation.
