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arXiv · 1705.05839

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

Jaiyul Yoo·Ruth Durrer
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Abstract

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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Jaiyul Yoo, Ruth Durrer. 2017-05-16. Gauge-Transformation Properties of Cosmological Observables and its Application to the Light-Cone Average. https://doi.org/10.1088/1475-7516%2F2017%2F09%2F016

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