Quantum-statistical effects of bosonic warm dark matter in microscopic interacting dark sectors

We investigate the impact of the quantum statistical properties of bosonic warm dark matter (BWDM) on a microscopic interacting dark-sector model mediated by a Yukawa coupling. We consider a BWDM scenario containing a Bose–Einstein condensed (BEC) component. By separating the BWDM phase-space distribution into thermal and condensate components, we derive the thermally averaged annihilation cross sections for the thermal–thermal, thermal–condensate, and condensate–condensate channels. The long-range scalar interaction and its Sommerfeld enhancement are included in the annihilation processes. We find that the condensate fraction provides an additional quantum-statistical degree of freedom controlling the microscopic dark-sector energy transfer. In particular, the transition between the thermal–thermal dominated regime and the condensate–condensate dominated regime is characterized by a critical condensate fraction r_c, which is mainly determined by the BWDM mass and the dark energy scalar field mass. For condensate fractions above this critical value, the condensate–condensate channel dominates the present-day interaction rate. By imposing the condition that the present-day interaction rate does not exceed the Hubble expansion rate, we determine the corresponding region of the dark-sector parameter space satisfying this condition.