Maxwell field with gauge fixing term in de Sitter space: Exact solution and stress tensor

The Maxwell field with a general gauge fixing (GF) term is nontrivial, not only the longitudinal and temporal modes are mixed up in equations, but also unwanted consequences might arise from GF term. We derive complete set of solutions de Sitter space, implement covariant canonical quantization which restricts residual transformation down to quantum transformation. Then, Gupta-Bleuler (GB) physical state, we calculate stress tensor amazingly independent constant invariant under transverse components simply same as those Minkowski spacetime, vacuum has one UV divergent ($\propto k^4$), becomes zero by 0th-order adiabatic regularization. longitudinal-temporal GB state due cancelation between parts. More interesting Its particle contribution its twice that minimally-coupling massless scalar field, containing $k^4$ $k^2$ divergences. After 2nd-order regularization, too, so there no need introduce ghost can be possible candidate for cosmological constant. Thus, all physics predicted will without carry out analogous calculation similar to, simpler than space.