Hierarchy of N-point functions in the Lambda CDM and ReBEL cosmologies

In this work we investigate higher-order statistics for the Lambda CDM and ReBEL scalar-interacting dark matter models by analyzing 180h(-1) Mpc dark matter N-body simulation ensembles. The N-point correlation functions and the related hierarchical amplitudes, such as skewness and kurtosis, are computed using the counts-in-cells method. Our studies demonstrate that the hierarchical amplitudes S-n of the scalar-interacting dark matter model significantly deviate from the values in the Lambda CDM cosmology on scales comparable and smaller than the screening length r(s) of a given scalar-interacting model. The corresponding additional forces that enhance the total attractive force exerted on dark matter particles at galaxy scales lower the values of the hierarchical amplitudes Sn. We conclude that hypothetical additional exotic interactions in the dark matter sector should leave detectable markers in the higher-order correlation statistics of the density field. We focused in detail on the redshift evolution of the dark matter field's skewness and kurtosis. From this investigation we find that the deviations from the canonical Lambda CDM model introduced by the presence of the "fifth" force attain a maximum value at redshifts 0.5 <z