Joint curvature and growth rate measurements with supernova peculiar velocities and the CMB

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 and DES-Dovekie) SN catalogues in combination with CMB data from Planck PR4 to constrain σ 8 in ΛCDM, 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 ± 0.22 ( 0 . 70 − 0.38 + 0.31 ) [ 1 . 02 − 0.45 + 0.38 ] for Pantheon+ (DES-Y5) [DES-Dovekie] in the base flat ΛCDM model. Interestingly, allowing for free γ and Ω k , we find hints of positive curvature: Ω k = − 0.011 ± 0.006 ( − 0 . 013 − 0.006 + 0.005 ) [ − 0 . 008 − 0.006 + 0.004 ] , which exclude flatness at 2.0 σ (2.6 σ ) [1.8 σ ], for the combination of CMB with Pantheon+ (DES-Y5) [DES-Dovekie]. 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 − 0.099 + 0.061 ( 0 . 500 − 0.098 + 0.054 ) [ 0 . 525 − 0.073 + 0.074 ], which are consistent with the predictions of General Relativity. 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 ΛCDM, we find that the H 0 tension is recast in terms of a significantly negative curvature and suppressed growth of structures.