Cosmological perturbations and invariant observables in geodesic lightcone coordinates

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...

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Bibliographic Details
Published in:Journal of cosmology and astroparticle physics 2022-01, Vol.2022 (1), p.34
Main Authors: Fröb, Markus B., Lima, William C.C.
Format: Article
Language:English
Subjects:
Coordinates
cosmological perturbation theory
Cosmological perturbation theory in GR and beyond
Einstein equations
Equations of motion
inflation
Invariants
Mathematical analysis
Observers
Perturbation theory
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Summary: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 non-linear 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.
ISSN:1475-7516
1475-7516
DOI:10.1088/1475-7516/2022/01/034