  While in the standard cosmological model the accelerated expansion of the
Universe is explained by invoking the presence of the cosmological constant
term, it is still unclear the true origin of this stunning observational fact.
It is therefore interesting to explore alternatives to the simplest scenario,
in particular by assuming a more general framework where the fluid responsible
of the accelerated expansion is characterised by a time-dependant equation of
state. Usually these models, dubbed dark energy models, are purely
phenomenological, but in this work we concentrate on a theoretically justified
model, the ghost dark energy model. Within the framework of the spherical
collapse model, we evaluate effects of dark energy perturbations both at the
linear and non-linear level and transfer these results into an observable
quantity, the mass function, by speculatively taking into account contributions
of dark energy to the mass of the halos. We showed that the growth rate is
higher in ghost models and that perturbations enhance the number of structures
with respect to the $\Lambda$CDM model, with stronger effects when the total
mass takes into account dark energy clumps.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics