Microscopic gauge-field conversion in the Big Beng cyclic cosmology: a renormalized proof of viability

We investigate a microscopic realization of the scalar-to-radiation conversion sector in the BigBeng cyclic cosmology. The phenomenological conversion term used in an earlier effective cycleis replaced by helicity-selective gauge production sourced by an axial scalar coupling, with thegauge modes, scalar background, trigger field, shear, and backreaction evolved simultaneously. Thegauge energy is treated with adiabatic ultraviolet subtraction, while the backreaction correlatoris evaluated in a specified finite reference prescription denoted R0. For a frozen benchmark withgauge group SU(3), Nf = Nan = 6, g = 2.70, yϕ = yχ = 0.60, and f/M∗ = 0.22, the anomalyrelation predicts λ = 2.51806169. The high-resolution evolution reaches ρ/ρc = 0.999076 with gaugefraction fA = 0.988262, scalar-plus-trigger fraction fϕ+χ = 0.011738, and negligible shear. Thechange in fA between the two principal resolutions is 1.68 × 10−4. We also quantify the finite-localrenormalization ambiguity of ⟨E·B⟩. An order-reduced sensitivity test shows that the local operatorproportional to q′′′/a4 can become dynamically important close to the high-density bounce, so thenear-bounce composition is not yet a scheme-independent ultraviolet prediction. The calculationtherefore establishes a reproducible proof of microscopic conversion viability in R0 and isolatesexplicit ultraviolet matching as the next theoretical bottleneck.