The quantization of linear gauge theories on curved spacetimes is subject to significant difficulties arising from the necessity of combining high-frequency aspects with gauge invariance and positivity. While the Maxwell and linearized Yang-Mills cases enjoy special features related to Hodge theory, linearized gravity appears to be even more subtle. In this talk I will present recent attempts based on Wick rotation and gauge fixing techniques, focusing on the example of linear perturbations of de Sitter space. While high-frequency aspects are efficiently dealt with with techniques of microlocal analysis, the final answer depends on unsolved problems in Fredholm theory and elliptic boundary value problems. The talk is based on on-going collaborations with Christian Gérard (Paris-Saclay) and Simone Murro (Genova).