  The assumption of collisionless cold dark matter on its own cannot reconcile
several astrophysical discrepancies (cusp-vs-core problem, missing satellite
problem, too-big-to-fail problem). Self-interacting dark matter provides a
promising framework for solving all these problems, and self-interaction cross
sections are duly constrained in the literature. Following the work of Tulin,
Yu, and Zurek [1], we can constrain the dark matter mass and the mass of a
light mediator assuming a generic scalar Yukawa-type interaction. In
particular, we constrain the strongly coupled inflationary dark matter of the
luminogenesis model, a unification model with the gauge group $SU(3)_C \times
SU(6) \times U(1)_Y$, which breaks to the Standard Model with an extra gauge
group for dark matter when the inflaton rolls into its true vacuum. The
luminogenesis model is additionally subject to constraints on inflation, and we
find an upper bound on the scale of symmetry breaking of the inflaton and the
decoupling scale $M_1$ of certain representations of the gauge group. We
emphasize that the luminogenesis model enables a unique connection between
astrophysical constraints, the nature of dark matter, and inflation.
