Reproductive freeze-in of self-interacting dark matter

We present a mechanism for dark matter (DM) production involving a self-interacting sector that at early times is ultrarelativistic but far underpopulated relative to thermal equilibrium (such initial conditions often arise, e.g., from inflaton decay). Although elastic scatterings can establish kinetic equilibrium we show that for a broad variety of self-interactions full equilibrium is never established despite the DM yield significantly evolving due to 2 -> k (k > 2) processes (the DM carries no conserved quantum number nor asymmetry). During the active phase of the process, the DM to Standard Model temperature ratio falls rapidly, with DM kinetic energy being converted to DM mass, the inverse of the recently discussed "cannibal DM mechanism." As this evolution is an approach from an out-of-equilibrium to equilibrium state, entropy is not conserved. Potential observables and applications include self-interacting DM signatures in galaxies and clusters, dark acoustic oscillations, the alteration of free-streaming constraints, and possible easing of sigma(8) and Hubble tensions.