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.
Keywords
Cite
@article{arxiv.1703.01158,
title = {Compactly supported linearised observables in single-field inflation},
author = {Markus B. Fröb and Thomas-Paul Hack and Atsushi Higuchi},
journal= {arXiv preprint arXiv:1703.01158},
year = {2017}
}
Comments
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