Reply to `Can infrared gravitons screen $Λ$?'

TL;DR

The paper argues that infrared gravitons can induce secular screening of the cosmological constant $\Lambda$ through quantum loops, and that Garriga and Tanaka's renormalization scheme for $R_{\rm ren}$ does not rule out this back-reaction. It shows that $R_{\rm ren}$ is not a properly defined composite operator and that the claimed constancy of $R$ does not follow, even in the presence of $\Lambda$, since a constant $R$ does not guarantee de Sitter expansion. Scalar models on non-dynamical de Sitter backgrounds exhibit large secular contributions to the stress tensor, illustrating that such effects can persist in more complete quantum gravity contexts. The authors advocate a Starobinsky-type stochastic formalism to sum leading infrared logs, enabling computation of gauge-invariant observables at leading order and providing a path toward nonperturbative quantum gravity predictions with potential relevance for inflationary dynamics and the observed smallness of $\Lambda$.

Abstract

We reply to the recent criticism by Garriga and Tanaka of our proposal that quantum gravitational loop corrections may lead to a secular screening of the effective cosmological constant. Their argument rests upon a renormalization scheme in which the composite operator $(R \sqrt{-g} - 4 Λ\sqrt{-g} )_{\rm ren}$ is defined to be the trace of the renormalized field equations. Although this is a peculiar prescription, we show that it {\it does not preclude secular screening}. Moreover, we show that a constant Ricci scalar {\it does not even classically} imply a constant expansion rate. Other important points are: (1) the quantity $R_{\rm ren}$ of Garriga and Tanaka is neither a properly defined composite operator, nor is it constant; (2) gauge dependence does not render a Green's function devoid of physical content; (3) scalar models on a non-dynamical de Sitter background (for which there is no gauge issue) can induce arbitrarily large secular contributions to the stress tensor; (4) the same secular corrections appear in observable quantities in quantum gravity; and (5) the prospects seem good for deriving a simple stochastic formulation of quantum gravity in which the leading secular effects can be summed and for which the expectation values of even complicated, gauge invariant operators can be computed at leading order.