A Simple, Exact Formulation of Number Counts in the Geodesic-Light-Cone Gauge
Abstract
:Author Contributions
Funding
Institutional Review Board Statement
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Data Availability Statement
Conflicts of Interest
Abbreviations
GLC | Geodesic Light-Cone |
FNC | Fermi Normal Coordinates |
Appendix A
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 . |
2 | In our previous paper [14], we applied the above integral in the limit of the small redshift bin . |
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. |
References
- Jeong, D.; Schmidt, F.; Hirata, C.M. Large-scale clustering of galaxies in general relativity. Phys. Rev. D 2012, 85, 023504. [Google Scholar] [CrossRef] [Green Version]
- Schmidt, F.; Jeong, D. Cosmic Rulers. Phys. Rev. D 2012, 86, 083527. [Google Scholar] [CrossRef] [Green Version]
- Kehagias, A.; Riotto, A. Symmetries and Consistency Relations in the Large Scale Structure of the Universe. Nucl. Phys. B 2013, 873, 514–529. [Google Scholar] [CrossRef] [Green Version]
- Bertacca, D.; Maartens, R.; Clarkson, C. Observed galaxy number counts on the lightcone up to second order: I. Main result. J. Cosmol. Astropart. Phys. 2014, 9, 037. [Google Scholar] [CrossRef] [Green Version]
- Kehagias, A.; Dizgah, A.M.; Na, J.N.; Perrier, H.; Riotto, A. A Consistency Relation for the Observed Galaxy Bispectrum and the Local non-Gaussianity from Relativistic Corrections. J. Cosmol. Astropart. Phys. 2015, 8, 18. [Google Scholar] [CrossRef] [Green Version]
- Ginat, Y.B.; Desjacques, V.; Jeong, D.; Schmidt, F. Covariant decomposition of the non-linear galaxy number counts and their monopole. J. Cosmol. Astropart. Phys. 2021, 12, 31. [Google Scholar] [CrossRef]
- Yoo, J.; Fitzpatrick, A.L.; Zaldarriaga, M. Three-point correlation of the Lyman-alpha forest: An optimal redshift space distortion estimator. Phys. Rev. D 2009, 80, 083514. [Google Scholar] [CrossRef] [Green Version]
- Yoo, J. A new relativistic N-body code for the clustering of cosmic neutrinos. Phys. Rev. D 2010, 82, 083508. [Google Scholar] [CrossRef] [Green Version]
- Challinor, A.; Lewis, A. The linear power spectrum of observed source number counts. Phys. Rev. D 2011, 84, 043516. [Google Scholar] [CrossRef] [Green Version]
- Bonvin, C.; Durrer, R. What galaxy surveys really measure. Phys. Rev. D 2011, 84, 063505. [Google Scholar] [CrossRef] [Green Version]
- Grimm, N.; Scaccabarozzi, F.; Yoo, J.; Biern, S.G.; Gong, J.-O. Precision cosmology with overlapping surveys: The importance of volume and cross-correlations. J. Cosmol. Astropart. Phys. 2020, 11, 64. [Google Scholar] [CrossRef]
- Scaccabarozzi, F.; Yoo, J.; Biern, S.G. Cross-correlation of future weak lensing surveys and Planck lensing data. J. Cosmol. Astropart. Phys. 2018, 10, 24. [Google Scholar] [CrossRef] [Green Version]
- Castorina, E.; Dio, E.D. Observing the cosmic acceleration with the Kilo-Degree Survey. J. Cosmol. Astropart. Phys. 2022, 1, 61. [Google Scholar] [CrossRef]
- Fanizza, G.; Gasperini, M.; Marozzi, G.; Veneziano, G. Generalized covariant prescriptions for averaging cosmological observables. J. Cosmol. Astropart. Phys. 2020, 2, 017. [Google Scholar] [CrossRef] [Green Version]
- Ellis, G. Relativistic cosmology. Gen. Rel. Grav. 2009, 41, 581–660. [Google Scholar] [CrossRef]
- Ellis, G.; Nell, S.D.; Maartens, R.; Stoeger, W.R.; Whitman, A.P. Ideal observational cosmology. Phys. Rep. 1985, 124, 315–417. [Google Scholar] [CrossRef]
- Fleury, P.; Clarkson, C.; Maartens, R. How does the cosmic large-scale structure bias the Hubble diagram? J. Cosmol. Astropart. Phys. 2017, 1703, 062. [Google Scholar] [CrossRef] [Green Version]
- Dio, E.D.; Durrer, R.; Marozzi, G.; Montanari, F. Galaxy number counts to second order and their bispectrum. J. Cosmol. Astropart. Phys. 2014, 1412, 17, Erratum in J. Cosmol. Astropart. Phys. 2015, 1506, E01. [Google Scholar] [CrossRef] [Green Version]
- Gasperini, M.; Marozzi, G.; Nugier, F.; Veneziano, G. Light-cone averaging in cosmology: Formalism and applications. J. Cosmol. Astropart. Phys. 2011, 1107, 008. [Google Scholar] [CrossRef] [Green Version]
- Ben-Dayan, I.; Gasperini, M.; Marozzi, G.; Nugier, F.; Veneziano, G. Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging. J. Cosmol. Astropart. Phys. 2012, 1204, 36. [Google Scholar] [CrossRef]
- Fleury, P.; Nugier, F.; Fanizza, G. Geodesic-light-cone coordinates and the Bianchi I spacetime. J. Cosmol. Astropart. Phys. 2016, 6, 008. [Google Scholar] [CrossRef] [Green Version]
- Ben-Dayan, I.; Gasperini, M.; Marozzi, G.; Nugier, F.; Veneziano, G. Average and dispersion of the luminosity-redshift relation in the concordance model. J. Cosmol. Astropart. Phys. 2013, 1306, 2. [Google Scholar] [CrossRef] [Green Version]
- Fanizza, G.; Gasperini, M.; Marozzi, G.; Veneziano, G. An exact Jacobi map in the geodesic light-cone gauge. J. Cosmol. Astropart. Phys. 2013, 11, 019. [Google Scholar] [CrossRef] [Green Version]
- Fanizza, G.; Gasperini, M.; Marozzi, G.; Veneziano, G. Observation angles, Fermi coordinates, and the Geodesic-Light-Cone gauge. J. Cosmol. Astropart. Phys. 2019, 1, 4. [Google Scholar] [CrossRef] [Green Version]
- Mitsou, E.; Scaccabarozzi, F.; Fanizza, G. Observed Angles and Geodesic Light-Cone Coordinates. Class. Quantum Grav. 2018, 35, 107002. [Google Scholar] [CrossRef] [Green Version]
- Fonseca, J.; Zazzera, S.; Baker, T.; Clarkson, C. The observed number counts in luminosity distance space. arXiv 2023, arXiv:2304.14253. [Google Scholar]
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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
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 StyleFanizza, 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