The halo mass function in interacting Dark Energy models

We present a detailed investigation of the effects that a direct interaction between Dark Energy (DE) and Cold Dark Matter (CDM) particles imprints on the Halo Mass Function (HMF) of groups and clusters of galaxies. Making use of the public halo catalogs of the {\small CoDECS} simulations, we derive the HMF for several different types of coupled DE scenarios both based on the FoF algorithm and on the SO halo identification for different values of the overdensity threshold $\Delta_{c}$. We compare the computed HMFs for coupled DE cosmologies with $\Lambda $CDM as well as with the predictions of the standard analytic fitting functions. Our results show that the standard fitting functions still reproduce reasonably well both the FoF and the SO HMFs of interacting DE cosmologies at intermediate masses and at low redshifts, once rescaled to the characteristic amplitude of linear density perturbations of each specific model as given by $\sigma_{8}$. However, we also find that such apparent degeneracy with $\sigma_{8}$ is broken both by the high-mass tail and by the redshift evolution of our HMFs, with deviations beyond $\sim 10%$ for most of the models under investigation. Furthermore, the discrepancy with respect to the predictions of standard fitting functions rescaled with the characteristic value of $\sigma_{8}$ shows -- for some models -- a strong dependence on the spherical overdensity threshold $\Delta_{c}$ used for the halo identification. We find that such effect is due to a significant increase of halo concentration at low redshifts in these models, that is however absent in the majority of the cosmological scenarios considered in this work. We can therefore conclude that the universality of the HMF is violated by cosmological models that feature a direct interaction between DE and CDM.