Erratum to: Distortions of Robertson–Walker metric in perturbative cosmology and interpretation as dark matter and cosmological constant

The Original Article was published on 20 February 2020

Erratum to: Eur. Phys. J. C (2020) 80:158 https://doi.org/10.1140/epjc/s10052-020-7713-4

This erratum concerns the corrections of Equation (41), that should read:

$$\begin{aligned} \langle A\rangle (\tau )=4\pi \left( \frac{1}{3}\mathcal {N}(n/\sqrt{3})-\frac{1}{n^2}\right) \frac{G\langle \tilde{\rho }_0\rangle }{H_0^2}a(\tau )^{n-1}, \end{aligned}$$

and Equation (44), that should read:

$$\begin{aligned} \mathcal {N}(n)=\frac{1}{n^2+1}-\frac{1}{n^2}, \quad \mathcal {M}(n)=\frac{1}{n^2-1}-\frac{1}{n^2}. \end{aligned}$$

These leads to corrections to subsequent Equations (45), (50), (51) and (53). The corrected formulas allows to evaluate the parameters as

$$\begin{aligned} n\cong 0.6761, \quad \Omega _{IM0}\cong 0.0402, \end{aligned}$$

which return a complete explanation of the dark matter \(\Omega _{FM0}\cong 0.272\cong \Omega _{DM0}\) and the dark energy \(\Omega _{F\Lambda 0}\cong 0.685\cong \Omega _{\Lambda 0}\).

The Equation (69) becomes

$$\begin{aligned} \Omega _{F\Lambda }(t)\cong {\left\{ \begin{array}{ll} unknown &{} for \; \mathbf{a} (t)<0.082 \\ 1 &{} for \; 0.082<\mathbf{a} (t)<0.867 \\ 0.685\cdot \mathbf{a} (t)^{-2.65} &{} for \; \mathbf{a} (t)>0.867 \end{array}\right. }. \end{aligned}$$

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Correspondence to Federico Re.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Re, F. Erratum to: Distortions of Robertson–Walker metric in perturbative cosmology and interpretation as dark matter and cosmological constant. Eur. Phys. J. C 81, 135 (2021). https://doi.org/10.1140/epjc/s10052-021-08935-x

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