Gauging away Physics

TL;DR

The paper critically analyzes the HM&M proposal that a nonlocal gauge transformation can remove the infrared divergence of the graviton propagator in de Sitter space by working in the Bunch-Davies vacuum. It demonstrates that the transformation effectively adds anti-sources at future infinity, thereby altering the propagator equation and the canonical commutation relations, which amounts to changing the underlying physics rather than performing a pure gauge manipulation. This modification yields a tensor power spectrum with a factor $[1 - e^{-\rho k}]$, implying an observable tilt and demonstrating that the approach cannot be a legitimate resolution of infrared issues in the MMC scalar or flat-space QED. Consequently, the work reinforces there is no de Sitter invariant state for dynamical gravitons within the standard framework and cautions against nonlocal gauge tricks that would distort fundamental observables and spectra, with broader implications for inflationary backreaction and the role of constrained fields.

Abstract

We consider the recent argument by Higuchi, Marolf and Morrison [1] that a nonlocal gauge transformation can be used to eliminate the infrared divergence of the graviton propagator, when evaluated in Bunch-Davies vacuum on the open coordinate submanifold of de Sitter space in transverse-traceless-synchronous gauge. Because the transformation is not local, the equal time commutator of undifferentiated fields no longer vanishes. From explicit examination of the Wightman function we demonstrate that the transformation adds anti-sources in the far future which cancel the bad infrared behavior but also change the propagator equation. The same problem exists in the localized version of the recent argument. Adding such anti-sources does not seem to be legitimate and could be used to eliminate the infrared divergence of the massless, minimally coupled scalar. The addition of such anti-sources in flat space QED could be effected by an almost identical gauge transformation, and would seem to eliminate the well known infrared divergences which occur in loop corrections to exclusive amplitudes.