Yang and Yeung (Chinese Journal of Physics 77, 1544, 2022) proposed that the present-day matter-antimatter asymmetry arises mainly from a highly suppressed detection probability for primordial antimatter, computed with an intuitive Feynman-propagator argument on a spatially flat FLRW cosmological background and yielding a suppression factor(a3(−τ)/a3(0))2≈10−6(a^3(-\tau)/a^3(0))^2 \approx 10^{-6}for a lepton-epoch example. The proposal is restricted to the post-inflationary hadron and lepton epochs, assumes the flat FLRW metric remains valid there, and leaves open whether the effect survives a complete quantum-field-theoretic treatment and whether it quantitatively accounts for the observed baryon asymmetry when combined with measured CP violation.

Background

The observable universe is made of matter, with no primordial antimatter found anywhere. The imbalance is quantified by the baryon-to-photon ratioηB≈6.1×10−10\eta_B \approx 6.1 \times 10^{-10}, measured consistently by both primordial nucleosynthesis and by the Planck satellite's analysis of the cosmic microwave background (Planck Collaboration 2020). Since 1967 the standard framework for explaining this asymmetry has been the Sakharov conditions: baryon number violation, C and CP symmetry violation (CP violation is the asymmetry, under the combined charge-conjugation and parity operation, between a process and its mirror process), and departure from thermal equilibrium. In this framework the asymmetry is a production asymmetry — the early universe generated slightly more baryons than antibaryons — and decades of work on electroweak baryogenesis, leptogenesis, and GUT baryogenesis have not yet produced a quantitatively confirmed mechanism; the CP violation measured in laboratories is many orders of magnitude too small, as reviewed by Dine and Kusenko (2004) and Canetti, Drewes, and Shaposhnikov (2012).

Yang and Yeung (2022) proposed an orthogonal mechanism: the asymmetry is not a production asymmetry at all but a detection asymmetry. Their starting point is the Dirac-Feynman-Stueckelberg interpretation of antimatter. The Dirac equation admits negative-energy solutions; Stueckelberg and Feynman reinterpreted a negative-energy particle state propagating backward in time as a positive-energy antiparticle propagating forward in time, and Feynman (1949) built the Feynman propagator — the time-ordered two-point function of the field — on this reinterpretation. In the standard reading, the backward-in-time negative-energy component is a calculational representation of an ordinary forward-in-time positive-energy antiparticle. Yang and Yeung instead treat the antiparticle's negative-energy wave function as a physical object propagating backward in time from its production event, literally into the smaller early universe.

For the background geometry they use the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) metric — the standard homogeneous and isotropic cosmological metric, with scale factora(T)a(T)describing cosmic expansion in cosmic timeTT. Spatial flatness is observationally established only back to photon decoupling (the cosmic microwave background era, about 380,000 years after the Big Bang); deeper in the thermal history (the quark epoch, the quark-gluon-plasma phase in which quarks and gluons were not yet confined into hadrons, the electroweak and grand-unified-theory or GUT epochs) the metric must be extrapolated. The authors introduce coordinatesX=a(T)xX = a(T)xthat separate cosmic expansion from local particle motion, argue the geometry is effectively Lorentzian for local propagation during the hadron epoch (roughly the first10−510^{-5}–10010^{0}s, with the paper's standard-thermal-history figures) and the lepton epoch (roughly the first 10 s, over which the paper takes the universe to expand by about a factor of ten), and write the Dirac Feynman propagator there. For an electron produced at time 0 and detected at timeτ\tau, the scale factor cancels out of the detection amplitude. For the positron, closing the frequency contour on the negative-energy pole and evaluating the wave-function 'collapse' at time−τ-\tau— when the universe was much smaller — leaves a factora3(−τ)/a3(0)a^3(-\tau)/a^3(0)in the amplitude, so the detection probability is suppressed by(a3(−τ)/a3(0))2≈10−6(a^3(-\tau)/a^3(0))^2 \approx 10^{-6}forτ=10 s\tau = 10\,\mathrm{s}. The interpretation: primordial antimatter wave functions recede into the tiny early universe and hardly overlap present-day detection wave functions, so primordial antimatter is essentially undetectable today, while primordial matter fills the present-day universe. The authors argue this picture is compatible with the Sakharov conditions and requires no new CP-violating physics.

The authors themselves flag what remains undone: the GUT and quark-gluon-plasma phases are excluded from the analysis; the validity of the flat FLRW metric in the thermal epochs is an assumption; the propagator treatment is presented as intuitive, with a full treatment via quantum field theory in curved spacetime or nonequilibrium quantum field theory not carried out; and no quantitative combination of the suppression with measured CP violation confronting the observed asymmetry is provided. The observational context makes the quantitative question sharp: no antimatter domains are allowed by annihilation gamma-ray bounds (Steigman 1976), and the antiprotons and positrons measured in cosmic rays by the Alpha Magnetic Spectrometer (AMS-02, Aguilar et al. 2016) are consistent with secondary production, so any surviving primordial-antimatter signal must lie below these measurements.

Problem Statement

Determine, within a complete quantum-field-theoretic framework, whether the detection probability of primordial antimatter in the present-day universe is suppressed relative to primordial matter by the mechanism of Yang and Yeung (2022), and whether that mechanism quantitatively accounts for the observed matter-antimatter asymmetry. The single objective — establishing the rigorous status and explanatory power of the detection-suppression mechanism — comprises three linked parts: (i) reformulate the propagation and detection of primordial particle-antiparticle pairs produced in the early universe within quantum field theory in curved spacetime or nonequilibrium quantum field theory, with an operational model of detection, and establish or refute the claimed suppression — the antimatter detection amplitude carryinga3(−τ)/a3(0)a^3(-\tau)/a^3(0)and hence a probability suppression(a3(−τ)/a3(0))2(a^3(-\tau)/a^3(0))^2while the matter amplitude is unsuppressed — including the possibility that the suppression is an artifact of the intuitive Feynman-propagator treatment; (ii) establish whether the conclusion extends across the primordial thermal history beyond the hadron and lepton epochs, into the GUT and quark-gluon-plasma phases, and whether it depends on the unverified extrapolation of the spatially flat FLRW metric to epochs below the CMB era; and (iii) if the suppression survives, combine it with measured CP-violation inputs to quantitatively reproduce the observed asymmetry — the baryon-to-photon ratioηB≈6.1×10−10\eta_B \approx 6.1 \times 10^{-10}and the absence of observable primordial antimatter — confronting any residual predicted primordial-antimatter flux with cosmic-ray and annihilation gamma-ray bounds. A rigorous refutation of the suppression within the complete framework is an admissible answer to parts (i) and (ii), and closes the question.

References

  1. Yi Yang and Wai Bong Yeung, 'Highly suppressed detection probability of the primordial antimatter in the present-day universe', Chinese Journal of Physics 77 (2022) 1544-1550, DOI 10.1016/j.cjph.2021.10.008, arXiv:2604.02388, https://arxiv.org/abs/2604.02388
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