# Propagators for gauge-invariant observables in cosmology

November 22, 2017

We make a proposal for gauge-invariant observables in perturbative quantum gravity in cosmological spacetimes, building on the recent work of Brunetti et al. [JHEP 08 (2016) 032]. These observables are relational, and are obtained by evaluating the field operator in a field-dependent coordinate system. We show that it is possible to define this coordinate system such that the non-localities inherent in any higher-order observable in quantum gravity are causal, i.e., the value of the gauge-invariant observable at a point $x$ only depends on the metric and inflation perturbations in the past light cone of $x$. We then construct propagators for the metric and inflaton perturbations in a gauge adapted to that coordinate system, which simplifies the calculation of loop corrections, and give explicit expressions for relevant cases: matter- and radiation-dominated eras and slow-roll inflation.

open access link
Class. Quant. Grav. 35 (2018) 095010

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@article{Frob:2017gyj,
author = "Fröb, Markus B. and Lima, William C. C.",
title = "{Propagators for gauge-invariant observables in
cosmology}",
journal = "Class. Quant. Grav.",
volume = "35",
year = "2018",
number = "9",
pages = "095010",
doi = "10.1088/1361-6382/aab427",
eprint = "1711.08470",
archivePrefix = "arXiv",
primaryClass = "gr-qc",
SLACcitation = "%%CITATION = ARXIV:1711.08470;%%"
}

Keywords:

*none*