Joint Curvature and Growth Rate measurements with Supernova Peculiar Velocities and the CMB

Abstract: 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 $σ<em>8$ 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 $γ= 0.519^{+0.061}</em>{-0.099}$ ($0.461<sup>{+0.085}_{-0.069}$), which are consistent with the predictions of General Relativity. In terms of $fσ<em>8(z)$, we find $fσ_8(0.024)=0.461^{+0.066}</em>{-0.035}$ ($$fσ<em>8(0.038) = 0.498^{+0.045}</em>{-0.050}$$) 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.