Light from the hottest stage of the universe has been traveling toward us for nearly 14 billion years. This is the cosmic microwave background — a faint glow filling the entire sky. Recently, astronomers noticed something odd: its polarization (the direction of oscillation of the electric field) appears rotated by about 0.3 degrees. As if someone had slightly turned an invisible knob.

The explanation may lie in the nature of dark energy — the mysterious force causing the universe to expand faster and faster. The authors of the study considered dark energy not as the usual scalar field but as a 3-form. This is a mathematical object similar to a field that fills space and, when expanding, behaves like a fluid. Its tensor structure allows it to interact with light in ways ordinary scalar fields cannot. As a result, the polarization of light can rotate — producing cosmic birefringence.

The scientists tested two interaction scenarios between the 3-form and photons — particles of light. The first, more complex (dimension-6 operator), requires an incredibly strong coupling to explain the observed 0.3-degree rotation. The second, simpler (dimension-4 operator), does the job, but at a cost: the photon acquires a tiny mass. This mass turns out to be comparable to the expansion rate of the universe — a quantity astronomers denote as H₀. Interestingly, the rotation profile as a function of distance (or time) in the second case is almost independent of the 3-form's potential shape, but sensitive to initial conditions. In the first case, it's the opposite.