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

TL;DR

This paper demonstrates that gauge dependence cancels out in the one-loop quantum corrections to the scalar field equation in de Sitter space, supporting gauge-independent cosmological observables.

Contribution

It shows the complete gauge dependence cancellation in quantum gravitational corrections to scalar fields in de Sitter, including new roles for external mode corrections.

Findings

Gauge dependence cancels when all diagram contributions are included.

External mode function corrections are crucial for cancellation.

Supports the construction of gauge-independent quantum gravitational observables.

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 $\Delta\alpha$ 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.