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arXiv · 2506.11260

Large-Scale-Structure Observables in General Relativity Validated at Second Order

Antoine Villey·Yonadav Barry Ginat·Vincent Desjacques·Donghui Jeong·Fabian Schmidt
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Abstract

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.

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Antoine Villey, Yonadav Barry Ginat, Vincent Desjacques, Donghui Jeong, Fabian Schmidt. 2025-06-12. Large-Scale-Structure Observables in General Relativity Validated at Second Order. https://doi.org/10.1088/1475-7516%2F2025%2F10%2F105

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