Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Cancellation of one-parameter graviton gauge dependence in the effective scalar field equation in de Sitter

Dražen Glavan, Shun-Pei Miao, Tomislav Prokopec, Richard P. Woodard

TL;DR

The paper tackles the gauge dependence of one-loop graviton corrections to the effective field equation for a massless, minimally coupled scalar on de Sitter space. By analyzing the Δα variation of the de Sitter-breaking graviton propagator, they show that gauge-dependent contributions cancel only when all one-loop 4-point diagrams and external mode-function corrections are included. The work extends flat-space gauge-independence techniques to cosmological spacetime, demonstrating that a gauge-independent effective self-mass can be extracted from the amputated 4-point function and used to obtain gauge-invariant quantum-corrected field equations. The results strengthen the prospects for constructing physically meaningful, gauge-independent cosmological quantum-gravitational observables, while outlining future checks involving the remaining gauge parameter β and potential Donoghue-identity generalizations.

Abstract

We investigate gauge dependence of one-graviton-loop corrections to the effective field equation of the massless, minimally coupled scalar in de Sitter, obtained by including source and observer corrections to the effective self-mass correcting the equation. Using the $Δα$ variation of the de Sitter-breaking graviton propagator in a one-parameter family of gauges, we compute the gauge-dependent contributions to the effective self-mass of a massless minimally coupled scalar mediating interactions between heavy scalars. We show that gauge dependence cancels provided the contributions from all diagram classes are collected, including one-loop corrections to external mode functions, which play a qualitatively new role relative to flat space. The resulting cancellation supports the construction of graviton gauge-independent cosmological quantum-gravitational observables from quantum-corrected effective equations.

Cancellation of one-parameter graviton gauge dependence in the effective scalar field equation in de Sitter

TL;DR

The paper tackles the gauge dependence of one-loop graviton corrections to the effective field equation for a massless, minimally coupled scalar on de Sitter space. By analyzing the Δα variation of the de Sitter-breaking graviton propagator, they show that gauge-dependent contributions cancel only when all one-loop 4-point diagrams and external mode-function corrections are included. The work extends flat-space gauge-independence techniques to cosmological spacetime, demonstrating that a gauge-independent effective self-mass can be extracted from the amputated 4-point function and used to obtain gauge-invariant quantum-corrected field equations. The results strengthen the prospects for constructing physically meaningful, gauge-independent cosmological quantum-gravitational observables, while outlining future checks involving the remaining gauge parameter β and potential Donoghue-identity generalizations.

Abstract

We investigate gauge dependence of one-graviton-loop corrections to the effective field equation of the massless, minimally coupled scalar in de Sitter, obtained by including source and observer corrections to the effective self-mass correcting the equation. Using the variation of the de Sitter-breaking graviton propagator in a one-parameter family of gauges, we compute the gauge-dependent contributions to the effective self-mass of a massless minimally coupled scalar mediating interactions between heavy scalars. We show that gauge dependence cancels provided the contributions from all diagram classes are collected, including one-loop corrections to external mode functions, which play a qualitatively new role relative to flat space. The resulting cancellation supports the construction of graviton gauge-independent cosmological quantum-gravitational observables from quantum-corrected effective equations.
Paper Structure (48 sections, 149 equations, 5 figures, 2 tables)

This paper contains 48 sections, 149 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The problem and the goal
  3. Reduction strategy
  4. General reduction
  5. One-loop reduction
  6. Feynman diagrams
  7. One-loop diagrams for 4-point functions
  8. Class 0.
  9. Class 1.
  10. Class 2.
  11. Class 3.
  12. Class 4.
  13. Class 5.
  14. Class 6.
  15. Class 7.
  16. ...and 33 more sections

Figures (5)

  • Figure 1: Eight classes of one-loop diagrams contributing to the $t$-channel of the connected four-point function, that is put on shell by the attached mode functions.
  • Figure 2: First line: diagram classe $\overline{\overline{4}}$ obtained by consolidating diagram classes in (\ref{['defV4a']})--(\ref{['defV4d']}), and class 2 in (\ref{['defV2a']})--(\ref{['defV2d']}), together with diagram $1a$ in (\ref{['defV1a']}). Second line: diagram class $\overline{5}$ obtained by consolidating diagrams from class 5 in (\ref{['defV5a']})--(\ref{['defV5d']}), and class 3 in (\ref{['defV3a']})--(\ref{['defV3b']}). The consolidated vertex $\overline{\text{B}}$, represented as a hatched vertex node, is defined in Eq. (\ref{['ConsolidatedBvertex']}).
  • Figure 3: One-loop diagrams representing contributions to the self-mass of the massive scalar field: the 3-vertex diagram ($I$) and the 4-vertex diagram ($I\!I$).
  • Figure 4: Three additional classes diagrams that contribute at the same order $(\kappa\lambda)^2$ to the $t$-channel 4-point function.
  • Figure 5: One-loop diagrams correcting the self-mass of the massive scalar from the interaction with the massless scalar: the 3-vertex diagram ($I\!I\!I$) and the 4-vertex diagram ($I\!V$).