De Sitter Breaking in Field Theory

TL;DR

The paper challenges the utility of manifest de Sitter invariance as an organizing principle for gauge theories on the inflationary background. It models inflation on the open conformal patch with $ds^2 = a^2(-d\eta^2 + d\vec{x}^2)$ and $a(\eta) = -1/(H\eta)$, and derives propagators for massless non-conformally invariant fields, notably the minimally coupled scalar $i\Delta_A(x;x')$ and the graviton propagator, highlighting infrared effects such as the $\ln(a a')$ secular terms. It shows that there are no normalizable de Sitter invariant states for these fields (Allen-Folacci for the scalar, perturbative graviton results) and that even if invariant propagators existed, infrared divergences would break de Sitter invariance, making invariant gauges physically dubious. Consequently, de Sitter breaking is essential to capturing observable inflationary quantum effects, and practical calculations should employ open-patch, noninvariant gauges rather than attempt full-manifold invariance.

Abstract

I argue against the widespread notion that manifest de Sitter invariance on the full de Sitter manifold is either useful or even attainable in gauge theories. Green's functions and propagators computed in a de Sitter invariant gauge are generally more complicated than in some noninvariant gauges. What is worse, solving the gauge-fixed field equations in a de Sitter invariant gauge generally leads to violations of the original, gauge invariant field equations. The most interesting free quantum field theories possess no normalizable, de Sitter invariant states. This precludes the existence of de Sitter invariant propagators. Even had such propagators existed, infrared divergent processes would still break de Sitter invariance.