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In this work we investigate higher order statistics for the $\lcdm$ and ReBELscalar-interacting dark matter models by analyzing $180\hmpc$ dark matterN-body simulation ensembles. The N-point correlation functions and the relatedhierarchical amplitudes, such as skewness and kurtosis, are computed using theCount-In-Cells method. Our studies demonstrate that the hierarchical amplitudes$S_n$ of the scalar-interacting dark matter model significantly deviate fromthe values in the $\lcdm$ cosmology on scales comparable and smaller then thescreening length $r_s$ of a given scalar-interacting model. The correspondingadditional forces that enhance the total attractive force exerted on darkmatter particles at galaxy scales lowers the values of the hierarchicalamplitudes $S_n$. We conclude that hypothetical additional exotic interactionsin the dark matter sector should leave detectable markers in the higher-ordercorrelation statistics of the density field. We focussed in detail on theredshift evolution of the dark matter field's skewness and kurtosis. From thisinvestigation we find that the deviations from the canonical $\lcdm$ modelintroduced by the presence of the ``fifth'' force attain a maximum value atredshifts $0.5<z<2$. We therefore conclude that moderate redshift data arebetter suited for setting observational constraints on the investigated ReBELmodels.

Hierarchy of N-point functions in the LCDM and ReBEL cosmologies