We consider a recent approach to the construction of gauge-invariant relational
observables in gravity in the context of cosmological perturbation theory. These observables
are constructed using a field-dependent coordinate system, which we take to be geodesic
lightcone coordinates. We show that the observables are gauge-independent in the fully nonlinear theory, and that they have the expected form when one adopts the geodesic lightcone
gauge for the metric. We give explicit expressions for the Sasaki-Mukhanov variable at linear
order, and the Hubble rate — as measured both by geodesic observers and by observers
co-moving with the inflaton — to second order. Moreover, we show that the well-known
linearised equations of motion for the Sasaki-Mukhanov variable and the scalar constraint
variables follow from the gauge-invariant Einstein’s equations
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:85195 |
| Date | 04 May 2023 |
| Creators | Fröb, Markus B., Lima, William C.C. |
| Publisher | IOP Publishing |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:article, info:eu-repo/semantics/article, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | 1475-7516, 034 |
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