Joint Curvature and Growth Rate measurements with Supernova Peculiar Velocities and the CMB
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arXiv
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2026
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| author | Crisman, Camilo Quartin, Miguel Rebouças, João |
| author_facet | Crisman, Camilo Quartin, Miguel Rebouças, João |
| contents | Type Ia supernova (SN) magnitudes present correlations due to the fact that their peculiar velocities are sourced by the large-scale structure of the Universe. This effect can be used to constrain properties related to the distribution and growth of matter perturbations. We analyze both Pantheon+ and Dark Energy Survey (DES-Y5) SN catalogues in combination with CMB data from Planck PR4 to constrain $σ_8$ in $Λ$CDM, optionally including both curvature and a modified growth index $γ$. We show that SN and CMB datasets are highly complementary and capable of measuring $σ_8$, $γ$ and $Ω_k$ simultaneously. Using only SN, we find $σ_8 = 0.73 \pm 0.22$ ($0.87 \pm 0.31$) for Pantheon+ (DES-Y5) in the base flat $Λ$CDM model. Interestingly, allowing for free $γ$ and $Ω_k$, we find hints of positive curvature: $Ω_k = -0.011 \pm 0.006$ $(-0.014 \pm 0.005)$, which exclude flatness at 2.2$σ$ (3.0$σ$), for the combination of CMB with Pantheon+ (DES-Y5). Such hints do not degrade if we also include a modified amplitude of CMB lensing, parametrized by $A_L$. We find that $γ= 0.519^{+0.061}_{-0.099}$ ($0.461^{+0.085}_{-0.069}$), which are consistent with the predictions of General Relativity. In terms of $fσ_8(z)$, we find $fσ_8(0.024)=0.461^{+0.066}_{-0.035}$ ($fσ_8(0.038) = 0.498^{+0.045}_{-0.050}$) for CMB + Pantheon+ (DES-Y5). Finally, the strong degeneracy between all three $Ω_k$, $γ$ and $H_0$ results in a broader CMB $H_0$ posterior. However, if we include SH0ES $H_0$ data, which is in known strong tension with the CMB in flat $Λ$CDM, we find that the $H_0$ tension is recast in terms of a significantly negative curvature and suppressed growth of structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_06361 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Joint Curvature and Growth Rate measurements with Supernova Peculiar Velocities and the CMB Crisman, Camilo Quartin, Miguel Rebouças, João Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology Type Ia supernova (SN) magnitudes present correlations due to the fact that their peculiar velocities are sourced by the large-scale structure of the Universe. This effect can be used to constrain properties related to the distribution and growth of matter perturbations. We analyze both Pantheon+ and Dark Energy Survey (DES-Y5) SN catalogues in combination with CMB data from Planck PR4 to constrain $σ_8$ in $Λ$CDM, optionally including both curvature and a modified growth index $γ$. We show that SN and CMB datasets are highly complementary and capable of measuring $σ_8$, $γ$ and $Ω_k$ simultaneously. Using only SN, we find $σ_8 = 0.73 \pm 0.22$ ($0.87 \pm 0.31$) for Pantheon+ (DES-Y5) in the base flat $Λ$CDM model. Interestingly, allowing for free $γ$ and $Ω_k$, we find hints of positive curvature: $Ω_k = -0.011 \pm 0.006$ $(-0.014 \pm 0.005)$, which exclude flatness at 2.2$σ$ (3.0$σ$), for the combination of CMB with Pantheon+ (DES-Y5). Such hints do not degrade if we also include a modified amplitude of CMB lensing, parametrized by $A_L$. We find that $γ= 0.519^{+0.061}_{-0.099}$ ($0.461^{+0.085}_{-0.069}$), which are consistent with the predictions of General Relativity. In terms of $fσ_8(z)$, we find $fσ_8(0.024)=0.461^{+0.066}_{-0.035}$ ($fσ_8(0.038) = 0.498^{+0.045}_{-0.050}$) for CMB + Pantheon+ (DES-Y5). Finally, the strong degeneracy between all three $Ω_k$, $γ$ and $H_0$ results in a broader CMB $H_0$ posterior. However, if we include SH0ES $H_0$ data, which is in known strong tension with the CMB in flat $Λ$CDM, we find that the $H_0$ tension is recast in terms of a significantly negative curvature and suppressed growth of structures. |
| title | Joint Curvature and Growth Rate measurements with Supernova Peculiar Velocities and the CMB |
| topic | Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.06361 |