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While in the standard cosmological model the accelerated expansion of theUniverse is explained by invoking the presence of the cosmological constantterm, 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 responsibleof the accelerated expansion is characterised by a time-dependant equation ofstate. Usually these models, dubbed dark energy models, are purelyphenomenological, but in this work we concentrate on a theoretically justifiedmodel, the ghost dark energy model. Within the framework of the sphericalcollapse model, we evaluate effects of dark energy perturbations both at thelinear and non-linear level and transfer these results into an observablequantity, the mass function, by speculatively taking into account contributionsof dark energy to the mass of the halos. We showed that the growth rate ishigher in ghost models and that perturbations enhance the number of structureswith respect to the $\Lambda$CDM model, with stronger effects when the totalmass takes into account dark energy clumps.

Effects of ghost dark energy perturbations on the evolution of spherical overdensities