How the Early Universe May Have Handed Matter Its Spin

In the first instants after cosmic inflation ended, the Universe underwent one of the most violent transformations in its history. The inflaton, the hypothetical scalar field that drove the exponential expansion of space, began to oscillate violently around the minimum of its potential, dumping its enormous energy into a hot soup of particles. A new theoretical study published in The European Physical Journal C by Ke Fu, Li-Shuang Liu, Yu-Feng Wang, Xin-Yu Gu and Xi-Bin Li of Inner Mongolia Normal University and their collaborators shows that this turbulent epoch, known as preheating, could have done something far stranger than simply making particles: it could have manufactured them with a built-in preference for one handedness over the other, an imbalance that cosmologists call helical asymmetry.

The mechanism hinges on a subtle piece of quantum field theory. The researchers considered a model in which a Dirac fermion, the class of matter particles that includes electrons and quarks, couples directly to the oscillating inflaton through a pseudoscalar Yukawa interaction. In plain terms, the coupling involves the gamma-five matrix, an object in the Dirac equation that distinguishes between the two possible spin orientations of a particle relative to its direction of motion. Because the inflaton field swings back and forth like a cosmic pendulum, the effective mass that the fermion experiences, which the authors call the pseudo-mass, repeatedly changes sign. Every time it crosses zero, the quantum vacuum becomes unstable and pairs of fermions are wrenched into existence, and crucially, the two helicity states are not created in equal numbers.

To make this statement precise, the team turned to the WKB approximation, a semiclassical technique borrowed from quantum mechanics in which wave functions are written as exponentials with slowly varying amplitude and phase. By matching the solutions on either side of each zero crossing of the pseudo-mass, they derived analytical expressions for the Bogoliubov coefficients, the mathematical objects that encode how many particles are produced in each quantum mode. The calculation, which involves parabolic cylinder functions, remains valid for an arbitrary number of successive production events, a significant advance over earlier treatments that could only handle a single pass of the oscillating field.

The key result is that the pseudoscalar coupling injects an imaginary contribution into the first-order adiabatic phase, denoted by the authors as the complex phase of the fermion mode. This imaginary piece depends on the helicity state of the particle, and it is solely responsible for breaking the symmetry between left- and right-handed fermions. When the coupling is switched off, the phase vanishes and the familiar helicity-symmetric result of standard fermionic preheating is recovered, with occupation numbers falling off as a clean Gaussian in momentum space. With the coupling present, that Gaussian is warped, and the two helicities peel apart in a way that can be computed exactly.

The researchers also identified a sharp boundary condition on where the asymmetry can live. Helical asymmetry is generated only for comoving momenta much smaller than a characteristic wavelength set by the fermion mass and the expansion rate of the Universe. Once a mode’s wavelength enters the corresponding horizon scale, the asymmetry is dramatically suppressed. This means the imbalance is fundamentally a large-scale phenomenon, imprinted on the longest wavelengths available in the early cosmos, precisely the scales that could matter for subsequent cosmological evolution.

Perhaps the most striking finding concerns coherence. In an expanding Universe, the authors show that the combined effects of parametric resonance and Pauli blocking, the quantum-mechanical exclusion principle that caps fermion occupation at one particle per mode, produce coherent enhancement in certain frequency bands and coherent suppression in others. Unlike bosons, whose occupation numbers grow exponentially through Bose enhancement, fermions can only be nudged up or down within strict limits. The real part of the complex WKB phase governs this coherent superposition, and the numerical simulations reveal that it significantly boosts the number density of each helicity state after roughly eight oscillations of the inflaton, a periodicity traced back to a numerical factor in the imaginary part of the phase.

The team validated their analytics with numerical simulations in both a static universe and an expanding one. In the static case, the helical asymmetry appears as isolated narrow resonance bands in momentum space, reminiscent of the instability bands familiar from bosonic preheating. When cosmic expansion is included, these bands wash out, but the deviation from Gaussian helicity distributions persists and grows with each successive production event. The authors also found that heavier fermions concentrate their production on smaller physical scales, and that massless fermions, consistent with earlier results on gravitational particle production, escape the mechanism entirely.

What elevates this work beyond a technical exercise is its potential connection to one of the deepest mysteries in cosmology: why the Universe contains vastly more matter than antimatter. Helicity-asymmetric fermion production is a natural ingredient in leptogenesis scenarios, in which an early asymmetry in neutrino-like particles is eventually converted into the baryon asymmetry we observe today. Because the mechanism identified by the authors does not depend on the precise value of the inflaton mass, it applies equally to low-scale inflationary models such as small-field and hybrid inflation, widening the range of theories in which such an asymmetry could have been seeded.

The framework is also extendable in directions that touch other observational frontiers. The authors note that the same WKB machinery can accommodate momentum-dependent pseudoscalar couplings, quantum chromodynamics effects, and electroweak interactions, and that helical fermion production may be linked to the generation of primordial magnetic fields, chiral gravitational waves, and even dark matter production in the early Universe. Each of these connections offers a potential observational handle on a process that unfolded when the cosmos was a fraction of a second old.

For now, the result remains theoretical, resting on analytical mathematics and numerical simulation rather than direct measurement. But it sharpens a growing realization among cosmologists that the transition from inflation to the hot Big Bang was not a passive fade but an active, symmetry-breaking crucible. If the inflaton really did couple to fermions through a pseudoscalar channel, the newborn Universe may have emerged from preheating with a slight but decisive twist, a handedness written into its matter content that echoes, in principle, all the way to the galaxies we see today.

Subject of Research: Helical asymmetry in fermionic preheating induced by a pseudoscalar Yukawa coupling between the inflaton and Dirac fermions after inflation

Article Title: Pseudoscalar Yukawa coupling induced helical asymmetry in fermionic preheating

Article References: Fu, K., Liu, L.-S., Wang, Y.-F., Gu, X.-Y., & Li, X.-B. (2026). Pseudoscalar Yukawa coupling induced helical asymmetry in fermionic preheating. The European Physical Journal C, 86(9), Article 1083. https://doi.org/10.1140/epjc/s10052-026-16298-4

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16298-4

Keywords: preheating, cosmic inflation, fermion production, helicity asymmetry, pseudoscalar Yukawa coupling, inflaton, WKB approximation, Bogoliubov coefficients, leptogenesis, baryogenesis, early universe, quantum field theory