Boltzmann hierarchies for self-interacting warm dark matter scenarios

Understand

We provide a general framework for self-interacting warm dark matter (WDM) in cosmological perturbations, by deriving from first principles a Boltzmann hierarchy which retains certain independence from a particular interaction Lagrangian.

• We consider elastic interactions among the massive particles, and obtain a hierarchy which is more general than the ones usually obtained for non-relativistic (as for cold DM) or for ultra-relativistic (as for neutrinos) approximations.
• The more general momentum-dependent kernel integrals in the Boltzmann collision terms, are explicitly calculated for different field-mediator models, including examples of a scalar field (either massive or massless) or a massive vector field.
• As an application, we study the evolution of the interaction rate per particle under the relaxation time approximation, and assess when a given self-interaction is relevant in comparison with the Hubble expansion rate.