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.Comment: 30 pp., 4 figures. Small typos fixed, refs adde
