The skewness of the distance-redshift relation in $\Lambda$CDM

TL;DR

This paper investigates the skewness in the distance-redshift relation within the $ ext{Lambda}$CDM model, attributing it mainly to late-time matter bispectrum effects and gravitational lensing perturbations.

Contribution

It applies a new framework for evaluating higher-order moments of cosmological observables to analyze skewness in the Hubble-Lemaître diagram, emphasizing the role of the matter bispectrum.

Findings

Skewness primarily originates from late-time matter bispectrum.

Gravitational lensing significantly contributes to distance perturbations.

Line-of-sight projection effects are sub-dominant.

Abstract

Starting from a recently proposed framework for the evaluation of the cosmological averages, we evaluate the higher-order moments for the distribution of a given observable. Then, we explicitly discuss the case of the Hubble-Lema\^itre diagram and evaluate its skewness at the leading order in the cosmological perturbative expansion of the gravitational potential. In particular, we focus on perturbations of the luminosity distance due to gravitational lensing. Finally, we discuss our findings in view of recent numerical relativistic simulations, confirming that the skewness in the Hubble-Lema\^itre diagram primarily originates from the late-time matter bispectrum, with other line-of-sight projection effects being sub-dominant.