We investigate cosmological constraints on an energy density contribution of elastic dark matter self-interactions characterized by the mass of the exchange particle and coupling constant. Because of the expansion behaviour in a Robertson-Walker metric we investigate self-interacting dark matter that is warm in the case of thermal relics. The scaling behaviour of dark matter self-interaction energy density shows that it can be the dominant contribution (only) in the very early universe. Thus its impact on primordial nucleosynthesis is used to restrict the interaction strength, which we find to be at least as strong as the strong interaction. Furthermore we explore dark matter decoupling in a self-interaction dominated universe, which is done for the self-interacting warm dark matter as well as for collisionless cold dark matter in a two component scenario. We find that strong dark matter self-interactions do not contradict super-weak inelastic interactions between self-interacting dark matter and baryonic matter and that the natural scale of collisionless cold dark matter decoupling exceeds the weak scale and depends linearly on the particle mass. Finally structure formation analysis reveals a linear growing solution during self-interaction domination; however, only non-cosmological scales are enhanced.
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