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Dark Matter (DM) models providing possible alternative solutions to thesmall- scale crisis of standard cosmology are nowadays of growing interest. Weconsider DM interacting with light hidden fermions via well motivatedfundamental operators showing the resultant matter power spectrum is suppressedon subgalactic scales within a plausible parameter region. Our basicdescription of the evolution of cosmological perturbations relies on a fullyconsistent first principles derivation of a perturbed Fokker-Planck typeequation, generalizing existing literature. The cosmological perturbation ofthe Fokker-Planck equation is presented for the first time in two differentgauges, where the results transform into each other according to the rules ofgauge transformation. Furthermore, our focus lies on a derivation of a broadlyapplicable and easily computable collision term showing importantphenomenological differences to other existing approximations. As one of themain results and concerning the small-scale crisis, we show the equalimportance of vector and scalar boson mediated interactions between DM andlight fermions.

Matter Power Spectrum in Hidden Neutrino Interacting Dark Matter Models: A Closer Look at the Collision Term