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

TL;DR

This paper demonstrates that interacting massive scalar quantum field theories in de Sitter space are perturbatively IR-stable with well-defined, de Sitter-invariant correlation functions that decay at large distances, applicable to various mass regimes.

Contribution

It proves the IR stability of the Hartle-Hawking vacuum in de Sitter QFT at all orders, including higher spin fields, under certain conditions.

Findings

Correlation functions are de Sitter-invariant and decay at large separations.

The Hartle-Hawking vacuum is perturbatively well-defined and IR-stable.

Results apply to scalars with masses in both the complementary and principal series.

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.