Baryogenesis from Temporal Gradient Asymmetry in the Fractal-Spectral Framework

Why is there more matter than antimatter? The Standard Model's CP violation is insufficient by orders of magnitude. This paper explores whether the fractal-temporal framework provides the missing ingredient. The mechanism is built on differential temporal coupling: if matter and antimatter couple to the τ-gradient field with a small CP-violating asymmetry ε_CP (analogous to the Jarlskog invariant in the CKM matrix but in the temporal sector), the non-equilibrium conditions of the early universe's desynchronization epoch generate a net baryon asymmetry. The three Sakharov conditions are addressed: baryon number violation through the fractal phase transition's symmetry-breaking properties (conjectured, not derived — stated as the weakest point), C and CP violation through the differential coupling, and departure from thermal equilibrium naturally provided by the desynchronization epoch where different spatial regions have different effective temperatures. The resulting baryon asymmetry η ~ ε_CP × g₀α²M_P/(T_c) × Δ_fractal reproduces the observed value η ≈ 6 × 10⁻¹⁰ for ε_CP ~ 10⁻⁵ — consistent with loop-level CP violation (α_w²/16π²). The mechanism requires no new particles or fields beyond the framework's existing temporal structure, and the departure from equilibrium is built in rather than requiring a first-order phase transition. The paper provides an honest comparison with standard mechanisms (electroweak baryogenesis, leptogenesis) via a detailed table: the temporal gradient approach has fewer new ingredients (no extended Higgs, no right-handed neutrinos) but rests on a weaker foundation (conjectured B violation, free ε_CP). The mechanism is explicitly characterized as a proof of concept — showing the framework contains the ingredients for baryogenesis — not a complete theory. Observational tests are indirect: if the fractal-spectral framework is confirmed through other channels (CMB signatures, dark matter profiles, gravitational waves with log-periodic spectrum from the phase transition), the baryogenesis mechanism gains support. The predicted baryon asymmetry is effectively uniform (δη/η ~ 10⁻¹⁰), consistent with observations but difficult to test directly. Open problems include microscopic derivation of baryon number violation, first-principles determination of ε_CP, competition with electroweak sphalerons, and gravitational wave spectrum from the fractal phase transition.