The model of the local Universe in the framework of the second-order perturbation theory

TL;DR

The paper addresses the Hubble tension by applying second-order perturbation theory to a dust+$\Lambda$ FLRW background and constraining the local metric with Cosmicflows-4 data. It develops a density-distribution model on a cubic lattice and derives the corresponding metric perturbations, then propagates light via null geodesics to study how the luminosity-distance relation $d_L(z)$ is affected. The authors show that inhomogeneities can dress the inferred $H_0$ from low-redshift data, with the effect depending on the amplitude $\Omega_{Virgo}$ and the background cosmology, and they find qualitative agreement with the distance-ladder $H_0$ in a $\Lambda$CDM setting, though the approach is at the edge of the second-order regime due to non-dust stress terms. These results highlight the importance of incorporating local inhomogeneities in interpreting low-redshift measurements of $H_0$, while also indicating the need for higher-order or more realistic energy-momentum descriptions to confirm the findings.

Abstract

Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann-Lemaitre-Robertson-Walker (FLRW) background filled with dust matter and a positive cosmological constant. In this paper, we use the Cosmicflows-4 (CF4) sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lemaitre-Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

Figures (7)

• Figure 1: Distribution of the galaxies within the elementary cell $x,y,z\in[-L,L]$, with $L=60\,\mathrm{Mpc}$. Black points - galaxies from the All CF4 Individual Galaxies. Color points - positions of the centers $(X_i,Y_i,Z_i)$ of the galaxy clusters under consideration: red - Virgo Cluster, green - Hydra Cluster, yellow - Formax Cluster, blue - Centaurus Cluster, magenta - Pavo Cluster.
• Figure 2: The isosurfaces of the probability distribution function $f$ for the parameters listed in the Table \ref{['Tab:parameters']}.
• Figure 3: The local value of the Lemaître-Hubble constant $H_0=\dot{d}/d$ for the two examplary background parameters $(\Omega_m,\Omega_\Lambda)$ and several values of the amplitude of the inhomogeneities labeled by the $\Omega_{Virgo}$ quantity described in the text.
• Figure 4: The $d_L(z)-z$ relation for $\Omega_m=0.3$, $\Omega_\Lambda=0.7$ and various amplitudes: $\Omega_{Virgo}=0.0$ - top left, $\Omega_{Virgo}=0.25$ - top right, $\Omega_{Virgo}=0.3$ - bottom left, and $\Omega_{Virgo}=0.4$ - bottom right.
• Figure 5: The $H_0$ as a function of $\Omega_{Virgo}$ for the background model with the parameters $\Omega_m=0.3$ and $\Omega_{\Lambda}=0.7$.