Dimensionally Regulated Graviton 1-Point Function in de Sitter

TL;DR

This work computes the finite, one-loop 1PI graviton 1-point function in a locally de Sitter background using dimensional regularization, obtaining a finite constant that acts as a cosmological-constant renormalization $\delta \Lambda$. The authors derive the Feynman rules in curved spacetime, express propagators in terms of $A$,$B$,$C$ scalar types, and evaluate the graviton and ghost loop contributions to show that all noncovariant pieces cancel. The main finding is that the entire one-loop effect can be absorbed into a counterterm, yielding a renormalized result of zero at this order; differentregularization/gauge choices affect the finite part but not the necessity of a counterterm. The method provides a framework for higher-loop back-reaction studies and other quantum gravitational corrections during inflation, and it can be extended to scalar self-energies, fermion self-energies, and modified gravity models.

Abstract

We use dimensional regularization to compute the 1PI 1-point function of quantum gravity at one loop order in a locally de Sitter background. As with other computations, the result is a finite constant at this order. It corresponds to a small positive renormalization of the cosmological constant.