Volume 655, November 2021
|Number of page(s)||28|
|Section||Cosmology (including clusters of galaxies)|
|Published online||19 November 2021|
Theoretical and numerical perspectives on cosmic distance averages
Aix Marseille Univ., CNRS, CNES, LAM, Marseille, France
2 Instituto de Física Teórica UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Spain
Accepted: 15 August 2021
The interpretation of cosmological observations relies on a notion of an average Universe, which is usually considered as the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) model. However, inhomogeneities may statistically bias the observational averages with respect to FLRW, notably for distance measurements, due to a number of effects such as gravitational lensing and redshift perturbations. In this article, we review the main known theoretical results on average distance measures in cosmology, based on second-order perturbation theory, and we fill in some of their gaps. We then comprehensively test these theoretical predictions against ray tracing in a high-resolution dark-matter N-body simulation. This method allows us to describe the effect of small-scale inhomogeneities deep into the non-linear regime of structure formation on light propagation up to z = 10. We find that numerical results are in remarkably good agreement with theoretical predictions in the limit of super-sample variance. No unexpectedly large bias originates from very small scales, whose effect is fully encoded in the non-linear power spectrum. Specifically, the directional average of the inverse amplification and the source-averaged amplification are compatible with unity; the change in area of surfaces of constant cosmic time is compatible with zero; the biases on other distance measures, which can reach slightly less than 1% at high redshift, are well understood. As a side product, we also confront the predictions of the recent finite-beam formalism with numerical data and find excellent agreement.
Key words: large-scale structure of Universe / distance scale / cosmology: theory / methods: numerical
© M.-A. Breton and P. Fleury 2021
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