Thermal gravitino and axino rate from AutoTherm

If ultrarelativistic supersymmetric particles are thermally produced in the early universe they would influence big-bang nucleosynthesis, dark matter and reheating constraints. While the basic framework for thermal gravitino and axino production is well established, the calculation is not completely settled. In this work, we revisit the problem using AutoTherm, a new tool which automates the computation of thermal rates from first-principles Thermal Field Theory, with control over the inherent theory uncertainty in Hard Thermal Loop resummation schemes. We demonstrate that the strict leading-order (LO) scheme, while unambiguous for hard momenta, can yield unphysical negative rates when extrapolated to soft momenta. To address this, we introduce a tuned scheme that ensures positivity and agreement with strict LO at high momenta, while avoiding gauge-dependent pathologies. We compare our results with existing parametrizations in the literature, identifying discrepancies and providing new, reliable fits for the gauge and Yukawa contributions to the gravitino and axino production rates. The choice of resummation scheme gives a theory uncertainty by a factor of about 1.5... 3 depending on the temperature, which has been underappreciated until now. This residual spread should be taken into account in precision cosmological analyses of gravitino/axino abundancies.