The IR stability of de Sitter: Loop corrections to scalar propagators

TL;DR

This paper calculates one-loop quantum corrections to scalar field propagators in de Sitter space, demonstrating their IR stability and decay behavior, which supports the well-defined nature of interacting de Sitter invariant vacua.

Contribution

It provides explicit integral representations for loop corrections to scalar propagators in de Sitter space, applicable across all relevant mass ranges, including renormalizable cases.

Findings

Interacting propagators decay at least as fast as expected at large distances.

Loop corrections are well-behaved and convergent in renormalizable dimensions.

In some cases, decay is faster than any free propagator with positive mass squared.

Abstract

We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions. Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of SO(D,1). In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections. These representations suffice to analytically extract the leading behavior of the 2-point functions at large separations and may also be used for numerical computations. The interacting propagators decay at long distances at least as fast as one would naively expect, suggesting that such interacting de Sitter invariant vacuua are well-defined and are well-behaved in the IR. In fact, in some cases the interacting propagators decay faster than any free propagator with any value of $M^2> 0$.