WIMP matter power spectra and small scale power generation

Dark Matter (DM) is generally assumed to be massive, cold and collisionless from the structure formation point of view. A more correct statement however is that DM indeed experiences collisional damping, but on a scale which is supposed to be too small to be relevant for structure formation. The aim of this paper is to present a Cold (although ``collisional'') Dark Matter particle whose matter power spectrum is damped and see whether it is distinguishable from standard candidates. To achieve this purpose, we calculate the collisional damping and free-streaming scales of neutralinos and non conventional candidates (say light particles heavier than ~1 MeV but lighter than O(10) GeV). The latter can be considered as Cold Dark Matter (CDM) particles in the sense that they become non relativistic before their thermal decoupling epoch. Unlike neutralinos, however, their linear matter power spectrum can be damped on scales of ~ 10^3 Msol due to their interactions. Since these scales are of cosmological interest for structure formation, we perform a series of numerical simulations to obtain the corresponding non linear matter power spectra P(k)_{nl} at the present epoch. We show that because of small scale regeneration, they all resemble each other at low redshifts, i.e. become very similar to a typical CDM matter power spectrum on all but the smallest scales. Therefore, even if lensing measurements at redshift below unity were to yield a P(k)_{nl} consistent with CDM models, this would not constitute a sufficiently robust evidence in favour of the neutralino to rule out alternative DM candidates.