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We present a detailed study of the collapse of a spherical matter overdensityand the non-linear growth of large scale structures in the Galileon ghostcondensate (GGC) model. This model is an extension of the cubic covariantGalileon (G3) which includes a field derivative of type$(\nabla_\mu\phi\nabla^\mu\phi)^2$ in the Lagrangian. We find that the cubicterm activates the modifications in the main physical quantities whose timeevolution is then strongly affected by the additional term. Indeed, the GGCmodel shows largely mitigated effects in the linearised critical densitycontrast, non-linear effective gravitational coupling and the virialoverdensity with respect to G3 but still preserves peculiar features withrespect to the standard $\Lambda$CDM cosmological model, e.g. both the linearcritical density contrast and the virial overdensity are larger than those in$\Lambda$CDM. The results of the spherical collapse model are then used topredict the evolution of the halo mass function, non-linear matter and lensingpower spectra. While at low masses the GGC model presents about 10% fewerobjects with respect to $\Lambda$CDM, at higher masses for $z>0$ it predicts10% ($z=0.5$)-20% ($z=1$) more objects per comoving volume. Using aphenomenological approach to include the screening effect in the matter powerspectrum, we show that the difference induced by the modifications of gravityare strongly dependent on the screening scale and that differences can be up to20% with respect to $\Lambda$CDM. These differences translate to the lensingpower spectrum where qualitatively the largest differences with respect to thestandard cosmological model are for $\ell<10^3$. Depending on the screeningscale, they can be up to 25% on larger angular scales and then decrease forgrowing $\ell$. These results are obtained for the best fit parameters fromlinear cosmological data for each model.

Growth of non-linear structures and spherical collapse in the Galileon Ghost Condensate model