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Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average

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arxiv 1705.05839 v2 pith:D3TH55JC submitted 2017-05-16 astro-ph.CO gr-qc

classification astro-ph.COgr-qc
keywords cosmologicalobservabletheoreticalaveragedescriptiondiffeomorphismsexpressiongauge-invariance
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Theoretical descriptions of observable quantities in cosmological perturbation theory should be independent of coordinate systems. This statement is often referred to as gauge-invariance of observable quantities, and the sanity of their theoretical description is verified by checking its gauge-invariance. We argue that cosmological observables are invariant scalars under diffeomorphisms and as a consequence their theoretical description is gauge-invariant, only at linear order in perturbations. Beyond linear order, they are usually not gauge-invariant, and we provide the general law for the gauge-transformation that the perturbation part of an observable does obey. We apply this finding to derive the second-order expression for the observational light-cone average in cosmology and demonstrate that our expression is indeed invariant under diffeomorphisms.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Observable Gravitational Wave Strain at Second Order

    gr-qc 2025-12 conditional novelty 7.0 of 10

    At second order, the gravitational-wave strain measured by geodesic observers exchanging light pulses is the transverse-traceless metric perturbation in the Newton gauge (h_N^(2)).

  2. Tetrad formalism for exact cosmological observables

    astro-ph.CO 2019-08 accept novelty 7.0 of 10

    The paper derives exact, coordinate-independent equations for cosmological observables on a new 'observer space-time' manifold, using tetrads to track the observer frame.

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