Correction: Christodoulou et al. A Common Origin of the H₀ and S₈ Cosmological Tensions and a Resolution Within a Modified ΛCDM Framework. Galaxies 2026, 14, 16

Missing Subsection

In the original publication [1], the Section 4.10, “Hubble Tension Unraveled” was inadvertently omitted from the manuscript. The missing subsection is provided below and has been added to the end of Section 4 in the updated version of the article.

4.10. Hubble Tension Unraveled

Rows 1 and 2 in Table 5 indicate that the values of $H_0$ and ${\mathsf{\Omega }}_{\mathsf{\Lambda }0}$ remain unchanged in $\gamma \mathsf{\Lambda }$CDM. On the other hand, Equation (45) with $\gamma \ll 1$ implies that the local CDL measurements infer an enlarged value of the Hubble constant

$$H_0\left(\gamma \right)=H_0\left(1+\gamma \right),$$

(92)

relative to the CMB-inferred value of $H_0=\left(67.4\pm 0.5\right)$ km ${\mathrm{s}}^{-1}$ ${\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$.

For the $\gamma$ values adopted in this work $(\gamma \simeq 4\%$–$8\%)$, the Hubble tension is thereby resolved. In Table 6, we summarize the $\gamma \mathsf{\Lambda }$CDM values of $H_0\left(\gamma \right)$ in comparison to the results of the two leading sets of local CDL measurements [15–17].

Table 6. $\gamma \mathsf{\Lambda }$CDM values of $H_0\left(\mathsf{\gamma }\right)$ (Equation (92) with $H_0=67.4$ km ${\mathrm{s}}^{-1}$ ${\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$) compared to the $H_0$ [CDL] results from local CDL measurements.

γ	⟶	${\mathit{H}}_0\left(\mathit{\gamma }\right)$ $\left(\mathbf{k}\mathbf{m} {\mathbf{s}}^{-1} {\mathbf{M}\mathbf{p}\mathbf{c}}^{-1}\right)$	${\mathit{H}}_0$ [CDL] $\left(\mathbf{k}\mathbf{m} {\mathbf{s}}^{-1} {\mathbf{M}\mathbf{p}\mathbf{c}}^{-1}\right)$	⟵	Data Set	Reference–Review
0.083		73.0	$73.0\pm 1.0$		Cepheids–SnIa	[16]–[15]
0.076		72.5	$72.5\pm 1.0$		Cepheids–SnIa (+TRGB)
0.039		70.0	$69.8\pm 1.7$		SnIa–TRGB	[17]–[15]
0.035		69.8

Table 6. $\gamma \mathsf{\Lambda }$CDM values of $H_0\left(\mathsf{\gamma }\right)$ (Equation (92) with $H_0=67.4$ km ${\mathrm{s}}^{-1}$ ${\mathrm{M}\mathrm{p}\mathrm{c}}^{-1}$) compared to the $H_0$ [CDL] results from local CDL measurements.

γ	⟶	${\mathit{H}}_0\left(\mathit{\gamma }\right)$ $\left(\mathbf{k}\mathbf{m} {\mathbf{s}}^{-1} {\mathbf{M}\mathbf{p}\mathbf{c}}^{-1}\right)$	${\mathit{H}}_0$ [CDL] $\left(\mathbf{k}\mathbf{m} {\mathbf{s}}^{-1} {\mathbf{M}\mathbf{p}\mathbf{c}}^{-1}\right)$	⟵	Data Set	Reference–Review
0.083		73.0	$73.0\pm 1.0$		Cepheids–SnIa	[16]–[15]
0.076		72.5	$72.5\pm 1.0$		Cepheids–SnIa (+TRGB)
0.039		70.0	$69.8\pm 1.7$		SnIa–TRGB	[17]–[15]
0.035		69.8

The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.