We describe a field‑level Bayesian reconstruction of the local cosmic velocity field and its exploitation for precision cosmology. Using the latest implementations of velocity‑field inference (Manticore‑Local, Carrick et al., Lilow et al., and related approaches) we generate a posterior ensemble of three‑dimensional velocity maps that are fully consistent with the observed galaxy distribution in the 2M++ catalogue. By forward‑modelling the mapping from true distances to observed redshifts we can directly compare these velocity fields with independent distance indicators—type Ia supernovae, Tully–Fisher measurements, and Cepheid‑based distances. The joint analysis yields constraints on the Hubble constant and on the amplitude of matter clustering (S₈), while explicitly propagating the uncertainties inherent in the velocity reconstruction.
A central focus of the talk is the treatment of systematic and selection effects that arise both in the reconstruction (e.g. galaxy bias, survey incompleteness, and non‑linear dynamics) and in the distance‑ladder data (e.g. calibration offsets, Malmquist bias, and host‑galaxy environment). We outline how these effects are incorporated into a coherent hierarchical likelihood, and we discuss the practical challenges encountered when coupling high‑dimensional field posteriors to sparse distance measurements.
Details of the methodology, validation, and cosmological implications are presented in the companion papers (Stiskalek et al. 2025a,b,c; McAlpine et al. 2025a)