Spherical collapse in the extended quintessence cosmological models
  We use the spherical collapse method to investigate the non-linear density
perturbations of pressureless matter in the cosmological models with the
extended quintessence as dark energy in the metric and Palatini formalisms. We
find that for both formalisms, when the coupling constant is negative, the
deviation from the $\Lambda$CDM model is the least according to the
evolutionary curves of the linear density contrast $\delta_{c}$ and virial
overdensity $\Delta_{v}$, and it is less than one percent. And this indicates
that, in the extended quintessence cosmological models in which the coupling
constant is negative, all quantities dependent on $\delta_{c}$ or $\Delta_{v}$
are essentially unaffected if the linear density contrast or the virial
overdensity of the $\Lambda$CDM model is used as an approximation. Moreover, we
find that the differences between different formalisms are very small in terms
of structure formation, and thus can not be used to distinguish the metric and
Palatini formalisms.
