Thermal Goldstino production with low reheating temperatures

We discuss thermal production of (pseudo) Goldstinos, the Goldstone fermions emerging from (multiple) SUSY-breaking sectors, when the reheating temperature is well below the superpartner masses. In such a case, the production during the matter-dominated era induced by the inflaton decay stage is more important than after reheating. Depending on the SUSY-breaking scale, Goldstinos are produced by a freeze-in or freeze-out mechanism via 1 -> 2 decays and inverse decays. We solve the Boltzmann equation for the momentum distribution function of the Goldstino. In the freeze-out case, Goldstinos maintain chemical equilibrium far after they are kinetically decoupled by elastic scatterings and, consequently, Goldstinos with different momentum decouple at different temperatures. As a result, their momentum distribution function shows a peculiar shape, and the final yield is smaller than if kinetic equilibrium were assumed. We revisit the cosmological implications in both R-parity-conserving and R-parity-violating supersymmetric scenarios. For the former, thermally produced Goldstinos can still be abundant enough to be dark matter at present times even if the reheating temperature is low, of order 1 GeV. For the latter, if the reheating temperature is low, of order 0.1-1 GeV, they are safe from the BBN constraints.