Peculiar velocity fields

Period: 2008 — present
Question: Can the motions of galaxies weigh the invisible Universe — and settle the Hubble constant?
Tracers: Tully–Fisher galaxies, Type Ia supernovae, Cepheids, gravitational-wave sirens
Data: 2M++, CosmicFlows, Pantheon+, SH0ES, GW170817
With: R. Stiskalek, D. Bartlett, H. Desmond, H. Courtois, M. Hudson, S. Mukherjee, J. Jasche

Galaxies do not sit still. Take the redshift of any nearby galaxy and it carries two things entangled together: the expansion of the Universe, and the galaxy's own drift through space — its peculiar velocity. Our own neighbourhood is no exception: the Local Group moves at roughly 600 km/s relative to the cosmic microwave background, and something has to be doing the pulling.

That something is mostly dark matter, and this is the point of the whole programme. Dark matter has never been seen through any photon it emits. But it pulls, and galaxies fall towards it, so the velocity field of galaxies is a map of all the mass — visible or not. Reading that map is hard: separating the drift from the expansion requires knowing each galaxy's distance independently of its redshift, and every distance indicator we have (the brightness of Type Ia supernovae, the rotation of spiral discs via the Tully–Fisher relation, the pulsing of Cepheid stars) comes with its own biases. Handle those carelessly and the map lies to you.

Building the toolkit

2008Lavaux et al. — how reconstruction methods get fooled, and by whatDOI arXiv
2010Lavaux, Tully, Mohayaee & Colombi — the origin of the CMB dipole flowDOI arXiv
2015Carrick, Turnbull, Lavaux & Hudson — the 2M++ prediction of the local flowDOI arXiv
2016Lavaux — VIRBIUS, Bayesian inference of the velocity fieldDOI arXiv
2019Graziani et al. — forward-modelling CosmicFlows-3DOI arXiv
2019Jasche & Lavaux — velocities from the BORG posteriorDOI arXiv
2020Boruah, Hudson & Lavaux — new peculiar velocities from supernovaeDOI arXiv
2021Boruah, Lavaux & Hudson — comparing velocity models and their systematicsDOI arXiv
2023Prideaux-Ghee et al. — field-level inference from the tracers aloneDOI arXiv

The programme began at the unglamorous end: a systematic catalogue of the ways velocity-field reconstructions get fooled — by survey edges, by sparse sampling, by the biases of the indicators themselves. That groundwork paid off when Lavaux and collaborators turned it on a simple question: is the mass we can map around us actually enough to explain the motion measured against the cosmic microwave background?

The cleanest answer came from the 2M++ compilation, a map of the galaxy distribution out to about 650 million light-years built for exactly this purpose. Gravity applied to that map predicts the Local Group should be moving at 540 ± 40 km/s, within ten degrees of the direction the CMB actually shows. The mass we can see accounts for most of the motion — but not all of it. The data prefer, at better than five sigma, an extra 160 km/s or so flowing in from beyond the edge of the map. The Universe outside the survey makes itself felt inside it.

From there the methods split into two complementary families: direct inference, treating the velocity field itself as the unknown and letting the distance data constrain it (VIRBIUS, then the forward-modelling of CosmicFlows-3, and eventually inference straight from the tracers with no galaxy survey at all); and cross-correlation, predicting velocities from a redshift survey and testing distance catalogues against them. Both now run on the posterior of BORG, which is what ties this page to the rest of the programme.

The Velocity Field Olympics

2026Stiskalek et al. — The Velocity Field Olympics, MNRAS 545DOI arXiv

By 2025 the field had a different problem: too many maps. Linear theory, machine-learning emulators, Bayesian forward models — each producing its own velocity field of the local Universe, each used somewhere to correct somebody's distances. Which one should you trust?

So the team held a competition. The Velocity Field Olympics puts every reconstruction through the same events, scored on how well it explains independent distance measurements it has never seen: Bayesian evidence, residual redshift errors, whether the map needs its velocities rescaled or an external flow bolted on to fit. The result is unambiguous — the non-linear Manticore/BORG reconstruction consistently outperforms the rest. As a by-product, cross-correlating density and velocity yields S₈ = 0.793 ± 0.035, in comfortable agreement with both weak lensing and Planck — a useful data point, since peculiar-velocity studies have historically been a source of outliers on exactly this number.

That matters beyond bragging rights: supernova and gravitational-wave cosmology both need a velocity model, and now there is a principled way to choose it.

The Hubble constant, three ways

2021Mukherjee et al. — velocity corrections for standard sirens, A&A 646DOI arXiv
2026Stiskalek et al. — H₀ from Cepheids alone, MNRAS 546DOI arXiv
2026Stiskalek et al. — no local H₀ anisotropy, MNRAS 546DOI arXiv

The expansion rate of the Universe today — the Hubble constant, H₀ — is the most contested number in cosmology: the early-Universe route and the local distance ladder disagree, stubbornly, at the several-sigma level. Peculiar velocities sit right in the middle of that argument, because every local measurement of H₀ must first subtract the drift from the expansion, and an unmodelled drift becomes a bias.

Three results show what careful velocity modelling changes. When a gravitational-wave event like GW170817 is used as a standard siren — the waveform gives the distance outright — the host galaxy's peculiar velocity is the dominant nuisance. A correction framework built by Mukherjee, Lavaux and collaborators revised H₀ for that event to 68.3 (+4.6/−4.5) km/s/Mpc.

More pointedly: the team rebuilt the distance ladder without its top rung. Drop the supernovae entirely, keep only Cepheid stars with geometric anchors and their host-galaxy redshifts, model the selection of the sample rigorously, and subtract the local flow with Manticore. The answer, H₀ = 71.1 ± 1.4 km/s/Mpc — a 1.8 % measurement from the ladder's second rung alone, with an error bar 41 % smaller than the previous analysis of the same data. It sits about 1.3σ below the supernova-based SH0ES value and 2.8σ above the cosmic microwave background prediction: the tension survives, but it is smaller from this route, and the result comes with an honest caveat that the exact selection assumptions can move it by up to one sigma.

And a claimed anomaly dissolved under the same treatment. Several groups had reported that H₀ appears anisotropic on the local sky — faster in some directions than others, which would break cosmology's founding assumption. The analysis does detect the directional signal, at high significance. But letting the model express a radially varying flow shows it for what it is: real, local, lumpy currents in the velocity field — not an anisotropic expansion. The inferred bulk flow is fully consistent with the standard cosmological model.

Where is the Local Group actually going?

2026Stiskalek et al. — Revisiting the Great Attractor, Open J. Astrophys. 9DOI arXiv

Since the 1980s, the standard story for our 600 km/s drift has had a villain: the Great Attractor, a huge mass concentration behind the southern Milky Way, dragging us in. The Manticore digital twin of the local Universe finally made it possible to re-ask the question properly — and the classical Great Attractor does not survive it.

The concept, it turns out, was three different questions wearing one name. What causes our velocity today? Not any single structure: all the mass within about 700 million light-years accounts for only 72 % of the speed, pointing 38 degrees away from where we are actually heading — the rest comes from further out. Where do the velocity streamlines converge? That depends entirely on the scale you smooth the map at: zoom in and flows converge on Virgo, zoom out and it is the Hydra–Centaurus region, further still and everything drains towards Shapley. And where will we end up? To answer that, the team ran the constrained simulations past the present day, ten times the current age of the expansion, into the far future. The dominant pull on the Local Group is the Virgo cluster — and even Virgo contributes at most a third of our velocity.

The Great Attractor, in other words, is an artefact of reading an instantaneous snapshot of a flowing Universe as if it were a map of destinations. No single attractor owns our motion; the whole neighbourhood does, and it took a full digital twin of that neighbourhood to say so.