Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter   spacetimes: Two-point functions and renormalized stress-energy tensors
  By considering Hadamard vacuum states, we first construct the two-point functions associated with Stueckelberg massive electromagnetism in de Sitter and anti-de Sitter spacetimes. Then, from the general formalism developed in [A. Belokogne and A. Folacci, Phys. Rev. D \textbf{93}, 044063 (2016)], we obtain an exact analytical expression for the vacuum expectation value of the renormalized stress-energy tensor of the massive vector field propagating in these maximally symmetric spacetimes. 
Andrei Belokogne, Antoine Folacci and Julien Queva
gr-qc hep-th math-ph math.MP