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Self-interacting dark matter has been proposed as a solution to thesmall-scale structure problems, such as the observed flat cores in dwarf andlow surface brightness galaxies. If scattering takes place through lightmediators, the scattering cross section relevant to solve these problems mayfall into the non-perturbative regime leading to a non-trivial velocitydependence, which allows compatibility with limits stemming from cluster-sizeobjects. However, these models are strongly constrained by differentobservations, in particular from the requirements that the decay of the lightmediator is sufficiently rapid (before Big Bang Nucleosynthesis) and fromdirect detection. A natural solution to reconcile both requirements areinelastic endothermic interactions, such that scatterings in direct detectionexperiments are suppressed or even kinematically forbidden if the masssplitting between the two-states is sufficiently large. Using an exact solutionwhen numerically solving the Schr\"odinger equation, we study such scenariosand find regions in the parameter space of dark matter and mediator masses, andthe mass splitting of the states, where the small scale structure problems canbe solved, the dark matter has the correct relic abundance and direct detectionlimits can be evaded.

Self-interacting inelastic dark matter: A viable solution to the small scale structure problems