Compactly supported linearised observables in single-field inflation

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.

33 pages, new section on the relation between our compactly supported observables and the scalar and tensor power spectra, agrees with published version up to appendix E

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• Approaches to linear local gauge-invariant observables in inflationary cosmologies
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• Gauge invariants of linearized gravity with a general background metric
• Graviton backreaction on the local cosmological expansion in slow-roll inflation
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• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor