Large-Scale-Structure Observables in General Relativity Validated at Second Order
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917082541588480 |
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| author | Villey, Antoine Ginat, Yonadav Barry Desjacques, Vincent Jeong, Donghui Schmidt, Fabian |
| author_facet | Villey, Antoine Ginat, Yonadav Barry Desjacques, Vincent Jeong, Donghui Schmidt, Fabian |
| contents | We present a second-order calculation of relativistic large-scale-structure observables in cosmological perturbation theory, specifically the "cosmic rulers and clock", which are the building-blocks of any other large-scale-structure observable, including galaxy number counts, on large scales. We calculate the scalar rulers (longitudinal perturbation and magnification) and the cosmic clock to second order, using a fully non-linear covariant definition of the observables. We validate our formulae on three non-trivial space-time metrics: two of them are null tests on metrics which are obtained by applying a gauge transformation to the background space-time, while the third is the "separate universe" curved background, for which we can also compute the observables exactly. We then illustrate the results by evaluating the second-order observables in a simplified symmetric setup. On large scales, they are suppressed over the linear contributions by $\sim 10^{-4}$, while they become comparable to the linear contributions on mildly non-linear scales. The results of this paper form a significant (and the most complicated) part of the relativistic galaxy number density at second order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_11260 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-Scale-Structure Observables in General Relativity Validated at Second Order Villey, Antoine Ginat, Yonadav Barry Desjacques, Vincent Jeong, Donghui Schmidt, Fabian Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology We present a second-order calculation of relativistic large-scale-structure observables in cosmological perturbation theory, specifically the "cosmic rulers and clock", which are the building-blocks of any other large-scale-structure observable, including galaxy number counts, on large scales. We calculate the scalar rulers (longitudinal perturbation and magnification) and the cosmic clock to second order, using a fully non-linear covariant definition of the observables. We validate our formulae on three non-trivial space-time metrics: two of them are null tests on metrics which are obtained by applying a gauge transformation to the background space-time, while the third is the "separate universe" curved background, for which we can also compute the observables exactly. We then illustrate the results by evaluating the second-order observables in a simplified symmetric setup. On large scales, they are suppressed over the linear contributions by $\sim 10^{-4}$, while they become comparable to the linear contributions on mildly non-linear scales. The results of this paper form a significant (and the most complicated) part of the relativistic galaxy number density at second order. |
| title | Large-Scale-Structure Observables in General Relativity Validated at Second Order |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.11260 |