# A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge

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## Abstract

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## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

GLC | Geodesic Light-Cone |

FNC | Fermi Normal Coordinates |

## Appendix A

## Notes

1 | This choice generalises the definition of the temporal gauge, already introduced in [21], such that it can be applied to the case of an arbitrary observer velocity ${v}_{\mu}$. |

2 | In our previous paper [14], we applied the above integral in the limit of the small redshift bin $\Delta {z}_{s}\to 0$. |

3 | The angular directions related to local observations (also used in [15,16]) are indeed those measured by a free-falling observer, and can be identified with the angles of the FNC system [24] where the metric is locally flat around all points of a given world line, with leading curvature corrections (which are quadratic) in the distance. |

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**MDPI and ACS Style**

Fanizza, G.; Gasperini, M.; Marozzi, G.
A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge. *Universe* **2023**, *9*, 327.
https://doi.org/10.3390/universe9070327

**AMA Style**

Fanizza G, Gasperini M, Marozzi G.
A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge. *Universe*. 2023; 9(7):327.
https://doi.org/10.3390/universe9070327

**Chicago/Turabian Style**

Fanizza, Giuseppe, Maurizio Gasperini, and Giovanni Marozzi.
2023. "A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge" *Universe* 9, no. 7: 327.
https://doi.org/10.3390/universe9070327