Three invisible strings oscillate in the intergalactic void. This is not poetry, but a hypothesis about the nature of dark matter — an ultralight quantum field with spin 1, carrying three polarizations. Unlike scalar models such as the axion, vector dark matter resembles a triple thread woven from oscillations of dark photons (as these particles are sometimes called). Back in the 1930s, Fritz Zwicky discovered invisible mass in galaxy clusters, initiating the search for dark matter. The inflation scenario, proposed by Alan Guth, provides a mechanism for the birth of such fields with an enhanced spectrum of fluctuations on small scales.
Tracking the evolution of the triple thread is made possible by numerical simulation: physicists solve the system of Schrödinger equations (first written by Erwin Schrödinger) and Poisson's equation for three complex components. Gravity, generated by the total density, causes waves to collapse into Bose-Einstein condensates — Proca stars. Simulations on a 512³ grid in cubes of size ~10⁻⁸ Mpc cover the era from radiation domination (redshift z~3.4×10⁵) to the matter era (z~790), showing how the large-scale structure forms.
The main result is the relation \(\tilde{M}_\star = (2.65\pm0.42) \tilde{M}_h^{0.64}\). It links the mass of the central core to the mass of the parent halo, with the exponent 0.64 noticeably steeper than predictions for scalar fields (usually 1/3). This difference directly reflects the contribution of additional polarization threads. A global polarization analysis showed that the fraction of the longitudinal mode drops from 58% to 32% over the simulation time, yielding to transverse components — the triple thread "unwinds" over time.
This first empirical law for vector dark matter is critical for predicting the merger rate of Proca stars. The steeper slope accelerates mergers, which could lead to enhanced gravitational-wave signals detectable by future instruments. The difference from the scalar case means that internal polarization threads leave an imprint on halo structure, opening a new way to test the nature of dark matter. Only about 10% of halos in the simulations contain confirmed Proca stars — the triple thread is selectively woven into the cosmic lace.
Thus, three invisible threads, twisted by inflation in the first moments after the Big Bang, weave into invisible stars. Their dance in the gravitational field of the halo remains to be decoded, but the first chords have already sounded.
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.