$S_8$ from peculiar velocities: agreement with Planck for Tully--Fisher and supernovae, tension for the fundamental plane

Richard Stiskalek

doi:10.1093/mnras/stag1266

paper

$S_{8}$ from peculiar velocities: agreement with Planck for Tully--Fisher and supernovae, tension for the fundamental plane

arXiv:2509.20235 · doi:10.1093/mnras/stag1266

Abstract

Peculiar velocity measurements constrain the parameter combination $f σ_{8}$ , the product of the linear growth rate $f$ and the fluctuation amplitude $σ_{8}$ . Under the approximation that $f$ is a monotonic function of $Ω_{m}$ , this can be related to $S_{8} \equiv σ_{8} Ω_{m} /0.3$ , enabling direct comparison with weak lensing and cosmic microwave background results. We use three classes of direct-distance tracers -- the Tully--Fisher relation, the fundamental plane, and Type Ia supernovae -- to infer peculiar velocities. A unified hierarchical forward model jointly calibrates each distance indicator and a linear theory reconstruction of the local Universe. This is the first consistent Bayesian analysis to treat all three major classes of distance indicators within a common framework, enabling cross-checks of systematics across diverse galaxy populations. Combining the Tully--Fisher and Type Ia supernova samples, we obtain $S_{8} = 0.798 \pm 0.035$ ( $f σ_{8} = 0.412 \pm 0.018$ ), in agreement with Planck and robust under the choice of galaxy bias model, with the uncertainty dominated by the variance of the 2M++ galaxy field. The fundamental plane constraints are instead unstable under the inhomogeneous Malmquist bias treatment; the quadratic extension preferred by the fundamental plane data drives their $S_{8}$ values lower. These findings indicate that low-redshift peculiar velocity data are concordant with the cosmic microwave background and do not reinforce the early-versus-late $S_{8}$ tension, though the fundamental plane results call for further scrutiny of their systematics.

arXiv comment12 pages, 7 figures. Accepted in MNRAS

S8​ from peculiar velocities: agreement with Planck for Tully--Fisher and supernovae, tension for the fundamental plane

Abstract

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$S_{8}$ from peculiar velocities: agreement with Planck for Tully--Fisher and supernovae, tension for the fundamental plane