Three invisible strings vibrate in the intergalactic void. That's not a poetic metaphor, but the physical reality of ultra-light vector dark matter: unlike a scalar field with a single degree of freedom, the vector field is described by three complex components — three threads. The mass of these particles, about 10⁻⁵ eV, is fantastically small: if you scaled an electron up to the mass of a person, the vector boson would be lighter than a feather. Back in the 1930s, Fritz Zwicky pointed out unseen mass in galaxy clusters, launching the quest for dark matter. While scalar models like the axion have been studied in detail, spin-1 vector fields — for example, dark photons — have only recently become the subject of full-scale numerical simulation. Their evolution in the expanding Universe, according to the inflation scenario of Alan Guth, generates a fluctuation spectrum enhanced on small scales, leading to early collapse and the formation of large-scale structure.
The dynamics of the vector field are governed by the system of Schrödinger equation and Law of Universal Gravitation (Poisson) for three complex components, where gravity is sourced by the total density. The evolution was solved using a pseudo-spectral method on a grid of up to 512³ in boxes with a dimensionless size of 26–40 (corresponding to ~10⁻⁸ Mpc for a field mass of 10⁻⁵ eV). Initial conditions were set by an analytic isocurvature spectrum from the inflation epoch with a characteristic peak. The simulation spanned from a=0.01 (z~3.4×10⁵, radiation era) to a≃4.3 (z≲790, matter era). Halos were identified by a spherical overdensity δ>25, and Proca stars at the centers by fitting the radial profile to a solitonic form (ϵ<0.5 dex).
The key result is the relation \(\tilde{M}_\star = (2.65\pm0.42) \tilde{M}_h^{0.6403\pm0.0235}\). The power-law index of 0.64 is steeper than the classic estimate of 1/3 derived from the Heisenberg uncertainty principle for a scalar field, but agrees with the maximum slope of 3/5 obtained in some cosmological simulations. The logarithmic scatter is 0.109 dex — a sign that merger history and environment play a significant role. The halo mass function shows additional suppression at low masses compared to the standard Sheth–Tormen formalism, and the fraction of halos with confirmed Proca stars does not exceed 50% and increases with mass. A global polarization analysis reveals a monotonic drop in the longitudinal fraction from 58% to 32% over the course of the simulation, while the transverse part grew — in agreement with earlier works. Inside individual halos, the spin density averaged in shells systematically increased as mass accreted, pointing to a buildup of local polarization, consistent with the condensate nature of the central clump.
The derived core–halo relation is the first empirical law for vector dark matter. It is crucial for computing the merger rate of Proca stars: a steeper slope accelerates mergers, which could lead to enhanced gravitational-wave signals or decays into Standard Model particles. The difference from the scalar case means that the internal polarization degrees of freedom leave an observable imprint on halo structure, opening a new way to probe the nature of dark matter.
Future simulations with larger volume, higher resolution, and the inclusion of self-interactions will refine the slope and its evolution with redshift. Of particular interest is the connection between deviations from the mean relation and merger history and local spin structure, which could serve as a bridge to multi-messenger astronomy.
The results directly impact the phenomenology of dark matter searches — from predictions for gravitational-wave observatories to laboratory experiments targeting dark photons.
A series of simulations with overlapping halo mass ranges and multiple realizations of initial conditions is planned to statistically confirm the law, as well as to compare it with predictions for scalar models in an identical cosmological setup.
The work touches on the fundamental question 'What is dark matter made of?' and paves a direct path to testing the vector nature of particles through small-scale astrophysics.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
We numerically studied the formation of structures from ultralight vector dark matter (spin 1) in the early Universe. Using pseudospectral simulations on a 512³ grid, we traced the evolution from the radiation era to the matter era, identifying halos and central solitonic cores (Proca stars). We derived a relation between core mass and halo mass with a slope of about 0.64 and investigated the polarization structure.
Where its strength is
The main strength lies in the first detailed cosmological simulation of a vector field, which revealed a nontrivial power-law relation between core mass and halo mass, distinct from the scalar case, and showed how the field's polarization evolves from longitudinal to transverse. This provides concrete predictions for the population of Proca stars and their observational signatures.
Where it could go next
Worth trying
Why this may matter
If vector dark matter indeed forms compact solitons at the centers of halos, this could explain certain excess gamma-ray signals and offer a new class of objects for multi-wavelength astronomy, linking early-Universe physics to current observations.
Nearby works in our archive
The closest work in the archive sits at 0.62 by meaning — the usual level for our corpus.
A typical Proca star with a field mass of 10⁻⁵ eV has the size of Neptune's orbit but weighs as much as a large asteroid — a teaspoon of material from its core would have a mass of tens of millions of tons.