Scheme dependence of quantum gravity on de Sitter background

TL;DR

This paper investigates how different quantization schemes affect IR effects and Lorentz invariance in quantum gravity on de Sitter space, highlighting the importance of specific matter redefinitions for preserving symmetry.

Contribution

It clarifies the scheme dependence of IR effects and Lorentz invariance in quantum gravity on de Sitter background, identifying conditions for symmetry preservation.

Findings

Lorentz invariance can be broken by arbitrary parametrizations.

Background metric shifts can eliminate metric parametrization effects.

Specific matter redefinitions preserve Lorentz invariance and are favored by unitarity.

Abstract

We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is also singled out by unitarity as the kinetic terms are canonically normalized.