# Gauge-transformation properties of cosmological observables and its application to the light-cone average

## 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 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.

- Authors:

- Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zürich, Winterthurerstrasse 190, CH-8057, Zürich (Switzerland)
- Département de Physique Théorique and Center for Astroparticle Physics, Université de Genève, Quai E. Ansermet 24, CH-1211 Genève 4 (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22667694

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 09; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COSMOLOGY; DISTURBANCES; GAUGE INVARIANCE; LIGHT CONE; PERTURBATION THEORY; VISIBLE RADIATION

### Citation Formats

```
Yoo, Jaiyul, and Durrer, Ruth, E-mail: jyoo@physik.uzh.ch, E-mail: ruth.durrer@unige.ch.
```*Gauge-transformation properties of cosmological observables and its application to the light-cone average*. United States: N. p., 2017.
Web. doi:10.1088/1475-7516/2017/09/016.

```
Yoo, Jaiyul, & Durrer, Ruth, E-mail: jyoo@physik.uzh.ch, E-mail: ruth.durrer@unige.ch.
```*Gauge-transformation properties of cosmological observables and its application to the light-cone average*. United States. doi:10.1088/1475-7516/2017/09/016.

```
Yoo, Jaiyul, and Durrer, Ruth, E-mail: jyoo@physik.uzh.ch, E-mail: ruth.durrer@unige.ch. Fri .
"Gauge-transformation properties of cosmological observables and its application to the light-cone average". United States.
doi:10.1088/1475-7516/2017/09/016.
```

```
@article{osti_22667694,
```

title = {Gauge-transformation properties of cosmological observables and its application to the light-cone average},

author = {Yoo, Jaiyul and Durrer, Ruth, E-mail: jyoo@physik.uzh.ch, E-mail: ruth.durrer@unige.ch},

abstractNote = {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 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.},

doi = {10.1088/1475-7516/2017/09/016},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 09,

volume = 2017,

place = {United States},

year = {Fri Sep 01 00:00:00 EDT 2017},

month = {Fri Sep 01 00:00:00 EDT 2017}

}