The puzzle
On scales of tens to hundreds of megaparsecs, the matter distribution of the universe is not uniform: galaxies, clusters, filaments, and voids form a cosmic web whose statistics are set by the initial conditions, the nature of dark matter, the gravitational theory, and the dark-energy expansion history. Measuring that web — both its instantaneous shape and how fast it is growing — pins down many of the most fundamental cosmological parameters and tests ΛCDM in a regime well removed from the CMB.
My group attacks this with three complementary handles: (i) the three-dimensional density field traced by galaxy redshift surveys; (ii) the peculiar velocities of nearby galaxies, which respond to that density field and so probe the growth rate of structure; and (iii) the weak gravitational lensing of distant background galaxies by intervening dark matter, which lets us image the structure directly — filaments and voids included.
Mapping LSS through galaxy surveys
Galaxies are biased tracers of the underlying dark-matter density field: where there is more dark matter, there are typically more galaxies. Galaxy redshift surveys therefore let us reconstruct the local density field, δm(x), as a function of position. The amplitude of clustering, σ8, can be measured from the galaxy two-point correlation function alone — modulo the galaxy bias b.
The bias degeneracy is broken by combining the reconstructed density field with observed peculiar velocities: galaxies should move in the direction the local gravity points them, with an amplitude proportional to the growth rate f(z) and the bias-weighted density. Comparing the predicted velocity field (from the redshift survey) to the observed velocity field (from distance indicators) directly measures fσ8(z ≈ 0). This is what we call cosmic flows.
See the Mapping LSS and Cosmic flows technique pages for the methods, the surveys we use, and the specific fσ8 measurements: Carrick et al. 2015 (0.401 ± 0.024, Tully–Fisher); Boruah et al. 2020 (0.400 ± 0.017, SNe Ia); and the most recent bias-corrected reanalysis Hollinger & Hudson 2024 (0.362 ± 0.023), which sits in tension with Planck.
Mapping LSS through weak gravitational lensing
Weak lensing distorts the shapes of background galaxies by intervening total mass — not just luminous matter — so it lets us image the cosmic web in dark matter directly. We apply this at three different scales of structure: the full cosmic-shear two-point statistics (the S8 measurement, discussed on the gravitational lensing technique page), individual dark-matter filaments, and individual voids.
Filaments of the cosmic web
Cosmological simulations predict that galaxies sit at the nodes of a vast filamentary network of dark matter. In Epps & Hudson 2017 we produced the first composite weak-lensing image of those filaments connecting galaxy halos — coverage at the University of Waterloo, CBC, and Newsweek. In Yang, Hudson & Afshordi 2020 we extended this by stacking weak-lensing mass and SDSS light around pairs of luminous red galaxies with ~8 h−1 Mpc projected separations. The filaments are not unusually dark: the inferred r-band mass-to-light ratio (M/L = 351 ± 137) and stellar mass fraction (M☆/M = 0.0073 ± 0.0030) are consistent with the cosmic mean and its predicted redshift evolution.
Cosmic voids
The vast under-dense regions between filaments and clusters leave a measurable signature in background-galaxy shapes — an outward tangential alignment around the void centre. Stacking the weak-lensing signal around many voids probes the behaviour of dark matter and dark energy in low-density environments and tests modified-gravity theories that screen in dense regions. See our 2026 MNRAS paper for the latest result.
Putting it together
Each probe carries different systematics. Galaxy clustering measures the bias-weighted matter power spectrum; peculiar velocities measure the growth rate at low redshift; weak lensing measures the projected total matter without any bias model. The combination cross-validates — and where it fails to, that tension is itself informative. See the S8 comparison on the dark-matter page: the peculiar-velocity and cosmic-shear analyses we have published lie modestly below and consistent-with the Planck CMB value respectively.
The near-term programme is to combine all three probes in a consistent joint analysis — UNIONS cosmic shear, the forthcoming 4HS peculiar velocity survey, and the next generation of density-field reconstructions — and to push individual measurements (filaments, voids) deep enough that they can discriminate between ΛCDM and modified-gravity alternatives on their own.