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Dark matter & small scales

Diffraction is sensitive to structure on scales that are dark but pristine, where baryons are neither a contaminant nor a window, which makes coherent sources an excellent probe of dark matter.

A diffraction pattern carries the shape of what made it, not just its size. An opening morphs through a circle, triangle, square, pentagon and hexagon at fixed area, and the pattern imprinted changes with it. The same applies to dark-matter halos: diffraction probes not only a halo's mass but the way that mass is distributed.

Accessing dark and pristine scales

The cosmological abundance of dark matter is known to sub-per-cent accuracy, but its distribution is only directly observed down to sub-galactic scales. Below about 106 M☉ halos go dark: their gravitational potentials are too shallow to hold enough baryons to form stars. That is a curse and a blessing at once: it makes light dark-matter halos a pristine testbed of dark-matter properties, insensitive to the complicated astrophysics that shapes larger structures.

Small scales are also where dark-matter scenarios are most easily told apart. Theories are selected to explain observations on large scales, and that leaves them considerable freedom below the size of a galaxy, where their predictions diverge: some suppressing small-scale structure (ultra-light and warm dark matter), others enhancing it (self-interacting particles, or primordial black holes[1] ). New probes of dark halos therefore have great potential to advance fundamental physics.[2]

Beyond the nature of dark matter itself, diffraction gives access to the initial conditions of the very early Universe. Many scenarios for the formation of cosmic structure (within the inflationary paradigm, for instance) predict an enhancement of the primordial fluctuations, which would leave small-scale halos denser and more abundant.[3] Any observation in that regime is a look into the Universe's earliest moments.

Fraction of dark matter in compact objects against object mass, from 10 to the minus 18 up to 10 to the 7 solar masses. Thin grey lines are individual limits, each labelled: evaporation, HSC, stars, quasars, gravitational waves from O3, supernovae, radio and dynamics. A single bright line traces the strongest limit at each mass, with everything above it shaded as excluded. Coloured bands along the bottom label which messenger reaches which mass range, from X-rays through visible and infrared to FRBs, ground-based gravitational waves and LISA.
Limits on the abundance of compact objects as a function of their mass, normalized by the dark-matter density. Thin grey lines are current limits, compiled in PBHbounds. Everything above them is ruled out. The coloured bands indicate the masses probed by each spectral range or observatory.

Coherent waves as microscopes

The sensitivity of diffraction is set by the wavelength of the coherent source, and each band reaches a different mass. Ground-based gravitational-wave detectors probe stellar- to intermediate-mass objects. Space-borne detectors are ideal for sub-galactic halos. At the longest wavelengths, the nanohertz waves seen by pulsar-timing arrays raise the possibility of “microlensing by galaxies”.[4] Radio sources are sensitive to planetary masses, with the potential not only to probe dark matter but to find extragalactic planets. At optical frequencies and above, wave optics becomes essential for asteroid-mass objects: a window in which all of the dark matter could still be compact objects.

What makes diffraction a distinctive probe is the richness of its signal. Because the source's frequency is measured, a diffraction pattern carries an unambiguous imprint of the lens's mass scale. It is also sensitive to how that mass is distributed, so observations can distinguish dark-matter profiles: the presence of a core in a halo,[5] or substructure within an object.[6] Some of those properties map directly onto theories: self-interacting dark matter predicts cores whose density is set by the interaction cross-section.[7] A coherent source can characterize an individual halo, much as a diffraction pattern characterizes a single slit, the figure at the top of this page.

A population, not one lens

A different regime emerges when halos are treated collectively, as microlensing treats populations of stars. The result is stochastic diffraction:[8] amplitude and phase fluctuations imprinted on every gravitational-wave event, whose statistical properties encode the properties of the halo population. Those fluctuations can be captured by an effective description and separated from the parameters of the source, which would let LISA[9] probe halos between 10 and 104 M☉, far below the mass of any individually detectable object, as forecast by Choi, Urrutia & Zumalacárregui.

Stochastic diffraction is present in every gravitational-wave signal. That is the sense in which the Universe has a dark timbre:[10] gravitational waves carry information about dark matter in the way a concert sounds different in an open-air stage and a concert hall.

Stochastic diffraction and the dark timbre. A frequency sweep through one realization of 2502 cold-dark-matter halos along the line of sight to a source at redshift 3. Stochastic diffraction probes mainly the halos within the Fresnel volume, highlighted here, which shrinks as the frequency rises. On the right, the real and imaginary parts of the amplification factor they produce.

Telling dark halos from stars

A dark halo is not the only thing that can diffract a gravitational wave. Stars and stellar remnants in a foreground galaxy produce signatures of the same kind, and at the masses ground-based detectors reach they are the dominant astrophysical systematic: an ordinary population of compact objects can imitate the dense halo predicted by self-interacting or ultra-light dark matter, or by a primordial black hole that has accreted one.[1] Separating the two is a precondition for any claim about dark matter, which is why the project treats those populations as a subject in their own right. See microlensing, where the same stars are the signal rather than the contaminant.

References

  1. B. Carr, A. J. Iovino, G. Perna et al., Primordial black holes: constraints, potential evidence and prospects Riv. Nuovo Cim. 49, 225 (2026)
  2. E. O. Nadler, K. K. Rogers, A. Drlica-Wagner, Dark matter constraints from small-scale cosmic structure (2026)
  3. T. Bringmann, D. Croon, S. Sevillano Muñoz, Updated constraints on the primordial power spectrum at sub-Mpc scales Phys. Rev. Lett. 137, 061002 (2026)
  4. D. L. Jow, U.-L. Pen, Measuring cosmic expansion with diffractive gravitational scintillation of nanohertz gravitational waves Phys. Rev. Lett. 134, 131001 (2025)
  5. G. Tambalo, M. Zumalacárregui, L. Dai, M. H.-Y. Cheung, Gravitational wave lensing as a probe of halo properties and dark matter Phys. Rev. D 108, 103529 (2023)
  6. S. Savastano, G. Tambalo, H. Villarrubia-Rojo, M. Zumalacárregui, Weakly lensed gravitational waves: probing cosmic structures with wave-optics features Phys. Rev. D 108, 103532 (2023)
  7. M. Kaplinghat, S. Tulin, H.-B. Yu, Dark matter halos as particle colliders: unified solution to small-scale structure puzzles from dwarfs to clusters Phys. Rev. Lett. 116, 041302 (2016)
  8. M. Zumalacárregui, Lens Stochastic Diffraction: A Signature of Compact Objects in Gravitational-Wave Data arXiv preprint (2024)
  9. LISA Collaboration, M. Colpi et al., LISA definition study report (2024)
  10. J. Urrutia, V. Vaskonen, Dark timbre of gravitational waves Phys. Rev. D 111, 123047 (2025)

Where this is done

Work packages
Dark-matter searches
Papers
Signatures of 10–10⁴ M☉ dark-matter halos in LISA via stochastic diffraction
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