Based on their observations of galaxies, clusters, and cosmic-scale filaments, astronomers are well aware that dark matter must account for some 80% of the universe’s total mass – even if physicists have yet to observe it directly. For decades, researchers aiming to uncover its true nature have treated dark matter as something reassuringly simple: a cold fluid which exerts no pressure, clumps together under its own gravity, and seeds the formation of galaxies.

Even with the emergence of compelling new dark matter candidates, such as ‘ultralight scalar fields’ that blur the line between particles and classical waves, this classical framework has continued to hold firm in cosmologists’ predictions. Regardless of the particles or mechanisms responsible for dark matter, researchers have assumed that it must perturb its gravitational surroundings in ways that allow theoretical predictions to be made about its influence on the universe, giving astronomers concrete signatures to search for in their observations.

Yet according to Prokopec and Vecchioni, the entire foundation of this approach could be far shakier than assumed. Their work asks a deceptively simple question: what actually changes when you take the quantum nature of dark matter seriously, rather than treating it as a purely classical field? If their conclusions are correct, they could reshape several assumptions that have been accumulating in the literature – including constraints on the very nature of dark matter that were thought to have already been established.

Ultralight dark matter refers to hypothetical particles with masses vastly smaller even than those of neutrinos – the lightest particles described by the Standard Model. If they exist, they would be so extraordinarily light that their quantum wavelengths would stretch across scales of thousands of light-years – as large as entire galaxies.

This wave-like behaviour would suppress the formation of smaller structures, potentially resolving long-standing tensions between real observations of dwarf galaxies and simulations of cold dark matter, which incorrectly predict that galaxies like the Milky Way should be surrounded by hundreds of small satellite galaxies. It would also mean that the field behaves less like a collection of particles and more like a coherently oscillating condensate – much like a Bose-Einstein condensate, an exotic state of matter in which quantum behaviours become visible on macroscopic scales.

To explore the possibility of ultralight dark matter in more detail, Prokopec and Vecchioni focus on a period of cosmic history called the matter-dominated era: an epoch which began just a few tens of thousands of years after the Big Bang, when the energy density of the universe came to be governed by non-relativistic matter rather than radiation. It was during this era that the seeds of large-scale structure truly began to grow.

Starting from small regions where dark matter was slightly more dense than its surroundings, these variations were amplified by gravitational instability over hundreds of millions of years, eventually collapsing into the filaments, sheets, and halos that host galaxies today. If ultralight dark matter was present during this era, its behaviour then is directly relevant to the structures we observe now.

To explore the possible role of ultralight dark matter in creating these structures, cosmologists have treated it as a classical wave with a well-defined amplitude and phase. As a result, the substance would behave like pressureless dust on large scales, but exert an oscillating pressure on small scales. These oscillations would then drive periodic changes in gravitational field strength at a frequency set by the particle’s mass.

In previous studies, researchers claimed that this prediction could be verified through observations of pulsar timing arrays. These networks of rapidly rotating neutron stars emit radio wave pulses with extremely predictable regularity, so that any shift in pulse arrival times must hint at some unseen gravitational influence.

Subsequent work went even further, claiming that oscillations in the ultralight dark matter background could impart a source of mass on gravitons: particles that quantum theories of gravity predict must exist as carriers of the gravitational force. If this were the case, it would amplify gravitational waves generated in other parts of the universe, leaving detectable signatures in the radio emissions of pulsar timing arrays.

In their study, Prokopec and Vecchioni set out to determine whether this amplification mechanism actually operates – and in turn, whether the constraints on dark matter derived from it can really be trusted.

The key innovation of the duo’s approach was to treat ultralight dark matter as a fully quantum field from the outset, rather than assuming it behaves classically. To do this, they describe the dark matter field using a general quantum state broad enough to capture its full range of possible behaviours: from a smooth, classical wave-like background to states with large quantum uncertainties in the field’s amplitude or momentum, as well as combinations of these. This generality ensured that their conclusions held regardless of the precise quantum state that ultralight dark matter actually occupies in nature.

To test the robustness of their results, Prokopec and Vecchioni tackle the same problem from two independent angles. In one approach, both the dark matter and the gravitational perturbations are treated as fully quantum objects; while in the other, the gravitational perturbations are treated as a classical but randomly fluctuating field while the dark matter retains its quantum description.

Despite these different starting points, both methods arrive at the same expression for how the dark matter background modifies gravitational wave propagation: a consistency check that substantially strengthens their results. Across the whole range of dark matter masses they considered, the duo verified that their approximations hold.

Altogether, the results of these calculations divide cleanly along the quantum-classical boundary – but neither side yields promising results for the amplification theory. For the classical condensate of ultralight dark matter, which most previous studies focused on, the impact on gravitational wave propagation is exactly zero: the graviton acquires no mass, and no amplification occurs, invalidating those earlier predictions.

The quantum nature of the dark matter field does generate a time-varying mass for the graviton. In principle, this could drive a powerful amplification effect known as parametric resonance, similar to pushing a swing at exactly the right moment to make it go higher and higher. Yet for ultralight dark matter within the range of masses that theorists consider viable, Prokopec and Vecchioni show that this effect is far too weak to produce any significant amplification. The quantum effect exists, but its influence is negligible.

The implications for ongoing observational efforts are significant. Until now, pulsar timing array constraints on ultralight dark matter have rested on the assumption that this amplification mechanism operates. But if the classical condensate has no effect and the quantum amplification is negligible, the gravitational wave enhancement those constraints depend on never actually occurs. Those constraints need to be revisited.

This doesn’t mean ultralight dark matter slips entirely out of reach of pulsar timing arrays, since an oscillating dark matter field has a direct effect on pulse arrival times. But the additional constraints derived from the assumed amplification of gravitational waves can no longer stand.

More broadly, the duo’s results could have profound implications for the methodologies used to study dark matter. The difference between treating it classically and quantum-mechanically can change the answer entirely: the classical part of the dark matter field contributes nothing to gravitational wave propagation, while the quantum part – routinely ignored until now – is the only part that has any effect at all, even if that effect is too small to observe. In other words, the standard classical approach does not merely give an approximate answer; in this context, it gives the wrong one.

These findings aren’t without precedent in Prokepec’s own work. In a 2024 paper, together with Leihua Liu at Jishou University in China, he tackled a strikingly similar question in the radiation-dominated era: the epoch preceding matter domination, in which the universe’s energy was dominated by photons and neutrinos travelling close to the speed of light. In this case, the duo asked whether gravitational waves in this era acquire a mass from their interactions with quantum fermionic matter such as neutrinos.

Here, a different but equally fundamental question arose: could gravitational waves themselves acquire a mass simply from propagating through the quantum matter that filled the early universe? On the face of it, this seemed possible. When physicists write down the equations governing gravitational waves in this environment, expanding the combined gravitational and matter equations to second order, mass-like terms appear – suggesting that the graviton, ordinarily required to be massless by general relativity, might behave differently in the hot, dense conditions of the early cosmos.

After careful calculation, the duo found they do not: the apparent mass was a mathematical artefact that vanished once the equations were solved correctly, using symmetry rules that follow directly from Einstein’s insight that the speed of light is the same for all observers. The result was initially met with some debate, but independent work by other groups has since reached the same conclusion, and a consensus has now formed. The graviton, in the radiation-dominated era at least, remains massless.

For Prokopec, the next frontier will be the density fluctuations that seed the temperature variations observed in the cosmic microwave background: the faint afterglow of the Big Bang, whose temperature pattern remains imprinted across the entire sky and has been mapped to extraordinary precision. Whether these fluctuations acquire a mass from interactions with a quantum matter background remains an open question that he is now actively pursuing. Together with his PhD student Daniel Frolovsky, Prokopec is also developing a quantum formalism for the dynamics of ultralight dark matter that could ultimately be used to study the formation of the universe’s large-scale structures within this new framework.

Ultimately, all of this work is united by a single, clarifying impulse: to test the assumptions that have quietly accumulated beneath some of cosmology’s most important observations, and to replace them with results rigorously derived from first principles.

Time and again, effects that seemed to complicate the picture of the early universe – masses appearing where there should be none, amplification mechanisms built into influential models – have turned out not to exist when placed under careful scrutiny. By stripping away what isn’t really there, Prokopec, Vecchioni, and their colleagues ultimately hope that a clearer understanding of the nature of dark matter can finally emerge.