Compactly supported linearised observables in single-field inflation

TL;DR

This paper constructs gauge-invariant, locally measurable observables in single-field inflation, showing their equivalence to better-behaved quantities like the linearised Weyl tensor, and clarifies the nature of infrared divergences as gauge artifacts.

Contribution

It introduces compactly supported gauge-invariant observables in single-field inflation and demonstrates their equivalence to local gauge-invariant quantities with improved infrared properties.

Findings

Gauge-invariant observables are equivalent to smeared linearised Weyl tensors.

Infrared divergences are gauge artifacts at tree level.

Results apply to Minkowski and de Sitter backgrounds.

Abstract

We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gauge-invariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observable and the smeared linearised Weyl tensor in Minkowski and de Sitter spaces. Our results indicate that the infrared divergences in the tensor and scalar perturbations in single-field inflation have the same status as in de Sitter space and are both a gauge artefact, in a certain technical sense, at tree level.