Wavelike Dark Matter, new physics invoking axions

All the matter that has ever been detected accounts for a mere 4.9% of the Universe. Most of the cosmos is the dark universe: a mix of dark matter (26.8%) and dark energy (68.3%), both of which have so far proved impenetrable puzzles.

The existence of dark matter has been inferred from the motion of stars since the 1930s, but its nature remains a mystery. Standard, thermally generated dark matter remains firmly undetected in laboratory searches for weakly interacting massive particles (WIMPs). The search is narrowing, and the possibilities are dwindling; physicists may soon have to move on to alternative explanations.

One of these explanations, as Tom Broadhurst puts it in an e-mail, “appears to be more viable than the long-standing, now almost disproven, expectation that some sort of new heavy particle – as none have been found in very stringent laboratory searches. This new approach is, in fact, quite the opposite: dark matter composed of very light bosons that are all in the ground state – a so-called Bose-Einstein condensate – and are the ultimate cold form of dark matter, where the wave state of the particles are all in phase and act as one giant wave that interferes with itself”.

A universe operating under the tenets of General Relativity requires Cold Dark Matter (CDM), a hypothetical particle (or set of particles) that moves slowly, does not interact with light, and interacts with ordinary matter primarily or solely through gravity. The existence of such a particle demands a theory that extends the Standard Model (SM) of particle physics, if not an entirely new theory that includes or unifies current physical theories. One extension of the SM, classified under supersymmetric theories, predicts the existence of WIMPs having rest-mass energies greater than 10 GeV. The lightest among the stable WIMPs has long been heralded as the most likely candidate for CDM. Laboratory searches, however, have failed to detect WIMPs through direct-detection or in collider experiments.

Let there be axions

At the opposite extreme in mass to WIMPs are axions: a broad class of particles that first appeared as a solution to charge-parity violation in the SM, but also in supersymmetric theories as well as theories with extra dimensions such as string theory (which seeks to unify all the four fundamental forces). Having rest-mass energies much smaller than 1 eV, these ultralight particles have no quantum-mechanical spin and therefore constitute bosons.

Early theoretical studies referred to axions as fuzzy dark matter, owing to the importance of quantum mechanical effects on such particles at macroscopic scales. The wave explanation for dark matter was proposed by Broadhurst and others in a highly cited paper in 2014 1. This was the first cosmological simulation employing ultralight bosons as CDM and confirmed the anticipated rich non-linear structure owing to self-interference of the wave function describing the mean field behaviour of these particles.

In a new work 2, the team explores the observational consequences of self-interfering waves that fully modulate the dark matter density throughout the halo on the de Broglie scale, one of the features of the wavelike dark matter.

A wavelike dark matter

In other words, they look for signatures of quantum behaviour on macroscopic scales: pervasive fluctuations in density ranging between zero (owing to completely destructive interference) and twice the local mean density (owing to perfectly constructive interference) on a characteristic scale, the de Broglie wavelength set by the boson mass. Thus, gravitational lensing should leave signatures in multiply-lensed images of background galaxies that reveal whether the foreground lensing galaxy inhabits a discrete or a wavelike dark matter halo. The team finds that, whereas discrete lens models leave well documented anomalies between the predicted and observed brightnesses and positions of multiply-lensed images, the new wavelike lens models correctly predict the level of anomalies left over by discrete lens models.

“An essential prediction for this form of matter is that there is a lot of interference forming a granulated structure and this causes lensing effects, meaning that background sources that lie beyond a lensing galaxy are magnified and deflected significantly compared to a smooth distribution of dark matter. In this new paper, we claim to have verified this unique distinguishing prediction, thereby making a strong case that dark matter is indeed a Bose-Einstein condensate with a long wavelength on galaxy scales”, explains Broadhurst.

To test the models further, the researchers used the quadruply-lensed triplet images in the system HS 0810+2554 as a benchmark and subjected the wavelike model to a battery of tests for reproducing them. The wavelike dark matter model was able to reproduce all aspects of this system, whereas the discrete one often fails.

The ability of wavelike dark matter to resolve lensing anomalies even in demanding cases like HS 0810+2554, together with its success in reproducing other astrophysical observations, tilt the balance toward new physics invoking axions.

“This is really a fundamental claim, and points to String Theory where such light bosons (axions) have been predicted as a possible dark matter candidate”, concludes Broadhurst.

Author: César Tomé López is a science writer and the editor of Mapping Ignorance

Disclaimer: Parts of this article may have been copied verbatim or almost verbatim from the referenced research paper/s.


  1. Schive, HY., Chiueh, T. & Broadhurst, T. (2014) Cosmic structure as the quantum interference of a coherent dark wave. Nature Phys doi: 10.1038/nphys2996
  2. Alfred Amruth, Tom Broadhurst, Jeremy Lim, Masamune Oguri, George F. Smoot, Jose M. Diego, Enoch Leung, Razieh Emami, Juno Li, Tzihong Chiueh, Hsi-Yu Schive, Michael C. H. Yeung, Sung Kei Li (2023) Anomalies in gravitational-lensed images revealing Einstein rings modulated by wavelike dark matter Nature Astronomy doi: 10.1038/s41550-023-01943-9

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