The IR stability of de Sitter QFT: results at all orders

Abstract: We show that the Hartle-Hawking vacuum for theories of interacting massive scalars in de Sitter space 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 QFTs 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.