Propagators for gauge-invariant observables in cosmology

Markus B. Fröb, William C. C. Lima
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
%%% contains utf-8, see: %%% add \usepackage[utf8]{inputenc} to your latex preamble @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;%%" }