Grey-body factors and thermodynamics of asymptotically de Sitter black holes in generalized Proca theory

Generalized Proca theory supplements gravity with a massive vector field whose derivative self-interactions can support black holes carrying primary vector hair. In the asymptotically de Sitter branch considered here, the de Sitter scale is effective: it is generated by the vector sector rather than imposed through a bare cosmological-constant term. We compute grey-body factors and effective absorption cross-sections for massive scalar, electromagnetic, and massless Dirac test fields on this background. The transmission curves are obtained from a sixth-order WKB barrier calculation and are compared with the quasinormal-mode reconstruction; the two descriptions mostly agree, with small visible differences at lower multipoles. Increasing the scalar mass raises and broadens the scalar barrier, suppresses transmission at fixed frequency, and shifts efficient transmission to higher frequencies. The couplings considerably affect the grey-body factors and black hole thermodynamics.