Can infrared gravitons screen $Λ$?

TL;DR

This work reevaluates the proposal that infrared gravitons in de Sitter space secularly screen the cosmological constant by scrutinizing gauge invariance. It demonstrates that the tadpole-corrected expansion rate $H_F$ is not a physical observable since it is not gauge invariant when the gauge parameter depends on the metric, undermining prior claims of screening. The authors then construct a gauge-invariant, smeared curvature observable using a window function $W(x)$ and a probe scalar with curvature coupling, showing that $ig\langle {\cal R}^{ren} \big\rangle_W = 4\Lambda\ \big\langle 1^{ren} \big\rangle_W$ for any $W$, implying no secular screening of the renormalized curvature to any order in perturbation theory. This establishes that, within pure gravity with a cosmological constant, the curvature-based expansion rate remains effectively constant, though it leaves open the possibility of other infrared effects in more general theories.

Abstract

It has been suggested that infrared gravitons in de Sitter space may lead to a secular screening of the effective cosmological constant. This seems to clash with the naive expectation that the curvature scalar should stay constant due to the Heisenberg equation of motion. Here, we show that the tadpole correction to the local expansion rate, which has been used in earlier analyses as an indicator of a decaying effective $Λ$, is not gauge invariant. On the other hand, we construct a gauge invariant operator which measures the renormalized curvature scalar smeared over an arbitrary window function, and we find that there is no secular screening of this quantity (to any given order in perturbation theory).