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.
Highlights
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
The studies within the cosmological perturbation theory up to second order yield that the influence of inhomogeneities on cosmological parameters inferred from a Hubble diagram can reach at most one percent level [1,2,3,4,5,6,7]
Similar results are reached by ray tracing into Newtonian N-body numerical simulations [8,9,10], relativistic N-body numerical simulations [11,12,13,14] or relativistic hydrodynamical numerical simulations of an inhomogeneous dust model [15,16,17,18,19,20]
Summary
The studies within the cosmological perturbation theory up to second order yield that the influence of inhomogeneities on cosmological parameters inferred from a Hubble diagram can reach at most one percent level [1,2,3,4,5,6,7]. Similar results are reached by ray tracing into Newtonian N-body numerical simulations [8,9,10], relativistic N-body numerical simulations [11,12,13,14] or relativistic hydrodynamical numerical simulations of an inhomogeneous dust model [15,16,17,18,19,20]. It is suggested that inhomogeneities manifest on the Hubble diagram through the emergence of spatial curvature during structure formation [21,22,23,24,25]
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