halos and complex sub-structures (e.g. @Davis1985 [@Bertschinger1998; @Springel2005]). These initial perturbations are thought to be (almost) Gaussian, created from quantum fluctuations during the inflation epoch and are the origin of all the objects seen in the Universe. The knowledge of the precise initial conditions and a comprehensive understanding of the underlying physical laws should, in principle, enable us to evolve these fluctuations forward in time and provide a test of the current models.

Most of the important features observable in the Universe today have grown via non-linear evolution from tiny primordial density perturbations. This makes the whole process of understanding their evolution complex and requires the use of techniques well beyond the linear perturbation theory [@Bernardeau2002]. Indeed, at scales below roughly $\unit[10]{Mpc}$ the evolution of structures had already entered the non-linear stage (i.e. the density contrast $\delta \rho$ is of order (or much greater) than the background density $\bar\rho$). The main resource available to cosmologists is the use of bigger and bigger cosmological simulations, most of them using the particle technique known as [$N$-body ]{}simulation [@Hockney1988; @Dehnen2011]. Numerical simulations may, for instance, help shed some light on the unknown nature of dark matter.

Clearly, the number of dark matter particles 