Infrared stability of de Sitter QFT: Results at all orders

We show that the Hartle-Hawking vacuum for any theory of interacting massive scalars on a fixed de Sitter background is both perturbatively well defined and stable in the IR. Correlation functions in this state may be computed on the Euclidean section and Wick rotated to Lorentz signature. The results are manifestly de Sitter-invariant and contain only the familiar UV singularities. More importantly, the connected parts of all Lorentz-signature correlators decay at large separations of their arguments. Our results apply to all cases in which the free Euclidean vacuum is well defined, including scalars with masses belonging to both the complementary and principal series of SO(D,1). This suggests that interacting Quantum Field Theories in de Sitter--including higher spin fields--are perturbatively IR stable at least when i) the Euclidean vacuum of the zero-coupling theory exists and ii) corresponding Lorentz-signature zero-coupling correlators decay at large separations. This work has significant overlap with a paper by Stefan Hollands, which is being released simultaneously.