Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude

Abstract

We construct an approximate solution to the cosmological perturbation theory around Einstein–de Sitter background up to the fourth-order perturbations. This could be done with the help of the specific symmetry condition imposed on the metric, from which follows that the model density forms an infinite, cubic lattice. To verify the convergence of the perturbative construction, we express the resulting metric as a polynomial in the perturbative parameter and calculate the exact Einstein tensor. In our model, it seems that physical quantities averaged over large scales overlap with the respective Einstein–de Sitter prediction, while local observables could differ significantly from their background counterparts. As an example, we analyze the behavior of the local measurements of the Hubble constant and compare them with the Hubble constant of the homogeneous background model. A difference between these quantities is important in the context of a current Hubble tension problem.

Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant

“…However, in the real Universe the pressure of the intra-cluster gas and the proper motions of the galaxy cluster members introduce departures from the energy-momentum tensor of the dust. In the previous paper [45], we estimated the upper bound of the uncertainty |∆T µ ν | ≈ 10 −6 ρ consistent with a typical value of the velocity dispersion of galaxies observed in galaxy clusters. In the matterdominated era, it is then justified to describe the matter content of the universe with the approximate energymomentum tensor T µ ν = ρ U µ Uν + ∆T µ ν satisfying this empirical constraint.…”

“…In the previous paper [45], we investigated perturbations around the Einstein-de Sitter (EdS) background, with Ωm = 1, ΩΛ = 0 and k = 0. The EdS scale factor is a (EdS) (t) = C t 2/3 .…”

“…The value of the constant C = 4.85 × 10 −3 can be found using the megaparsec as a unit of length, considering normalization a (EdS) (t0) = 1 and calculating the age of the EdS universe t0 for the Lemaître-Hubble constant value H0 = 67.37 [km/s/Mpc] taken from the Planck data [1]. In the current notation, the respective metric function from the work [45] is A10(t) = t 2/3 . It is easy to check that this form of A10(t) follows from (13), when α = 10 9 C 2 = 2.61 × 10 −5 .…”

Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant

“…In both papers [43,44] a decaying mode was considered. The subsequent paper [45] was dedicated to the analysis of the growing mode and the fourth-order perturbations were taken into account. Since a high order perturbations were present, a relatively large amplitude of the inhomogeneities was admissible.…”

“…Since a high order perturbations were present, a relatively large amplitude of the inhomogeneities was admissible. The papers [43][44][45] considered a spatially flat background without the cosmological constant. The main purpose of the present paper is to generalize these results such that the considered background could be any FLRW cosmological model filled with dust, with possibly non-vanishing spatial curvature, and with a positive cosmological constant.…”