  We consider a curvaton scenario in which the late-time domination and the
generation of the curvature perturbation is achieved by a non-oscillatory (NO)
curvaton potential. Instead of considering the conventional curvaton
oscillation, we consider ``weak trapping'' after preheating, which modifies the
evolution of the curvaton density after preheating. The primordial isocurvature
perturbation related to the curvaton is once converted into the fluctuation of
the number density of the preheat field through inhomogeneous preheating. Then
the evolution of the curvatons and the preheat field is controlled by the
preheat-field number density. The density of these fields decreases slightly
slower than the standard matter density which suggests that these fields will
grow with time. Finally, the preheat field decays to reheat the Universe
leaving behind the curvature perturbation. In our scenario the task of the
standard curvaton is not executed solely by the curvaton itself but is
partially shared with the preheat field. NO curvatons can be considered as the
hybrid version of the quintessential inflationary model.
