Large-scale-structure observables in general relativity validated at second order

Journal article

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 formulæ 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 ∼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.

Authors: Villey, A; Ginat, YB; Desjacques, V; Jeong, D; Schmidt, F

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: IOP Publishing
• Journal: Journal of Cosmology and Astroparticle Physics
• Volume: 2025
• Issue: 10
• Article number: 105
• Publication date: 2025-10-29
• Acceptance date: 2025-09-15
• DOI: 10.1088/1475-7516/2025/10/105
• EISSN: 1475-7516
• ISSN: 1475-7516
• Language: English
• Keywords: cosmological perturbation theory; galaxy clustering; Cosmological perturbation theory in GR and beyond; redshift surveys