De Sitter Breaking through Infrared Divergences

TL;DR

This work shows that de Sitter invariance does not guarantee de Sitter invariant propagators due to infrared divergences in curved spacetime QFT. By examining scalar and vector propagators on de Sitter space, the authors demonstrate that naive invariant mode sums are IR divergent for broad mass ranges and that dimensional regularization can falsely suggest invariant solutions. The correct approach, either via a compact spatial manifold or less singular vacua, yields infrared corrections that break de Sitter invariance but render propagators well-defined. These findings clarify infrared issues in inflationary contexts and have implications for the treatment of gravitons and other higher-spin fields in de Sitter backgrounds.

Abstract

Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with $M_S^2 < 0$, and for massive transverse vectors with $M_V^2 \leq -2 (D-1) H^2$, where $D$ is the dimension of spacetime and $H$ is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.