  We study the nonlinear stage of preheating in a model consisting of a single
inflaton field $\phi$ nonminimally coupled to the spacetime curvature and
considering a self-coupling quartic potential V ($\phi$) = $\lambda \phi^4/4$.
As the first motivation, we mention that this nonminimally coupled model agrees
with the observational data. The second and the central issue of the present
work is to exhibit aspects of wave turbulence associated with the mechanism of
energy transfer from the inflaton field to the inhomogeneous fluctuations
towards a state of thermalization. The imprints of the turbulence phase are
mainly shown in the power spectra in time and wavenumber of relevant quantities
such as the variance and the energy density of the inflaton field. We performed
the simulations for several values of the nonminimally coupled models and
taking into account the backreaction of the inflaton fluctuations in the
dynamics of the Universe, and that allowed to determine the effective equation
of state.
