Dark matter self-interactions in the matter power spectrum

We study the imprints of secluded dark sectors with a mass gap and self-interactions on matter power spectrum. When Dark Matter (DM) is sufficiently light, in ballpark few KeV, self-interacting we find qualitative difference respect to $\Lambda$CDM also free streaming DM. In order emphasize role interactions for evolution primordial perturbations discuss various regimes: ranging from ideal case tightly coupled perfect fluid Warm Matter, including realistic small but non-vanishing self-interactions. compute spectrum all these regimes aid Boltzmann solvers. Light are efficiently constrained by Lyman-$\alpha$ data that presence relaxes bound DM mass. As concrete realization models QCD-like sectors, where made light dark-pions.