Breaking Conformal Invariance in a Contracting Phase: Coupling-Driven Magnetogenesis at a Bounce

Maxwell theory in four dimensions is conformally invariant, so a smoothly contracting or expanding universe by itself creates no magnetic field from vacuum fluctuations; the coupling between electromagnetism and the background must break the symmetry. This paper studies the standard breaking, a time-dependent coupling function multiplying the electromagnetic action, during the contracting phase of a bounced cosmology. Contraction from a scale factor of 1e-3 to the turnaround spans a factor 1.20e+19, or 4.39e+01 e-folds. Within the stated power-law coupling model, an exponent of two in the coupling function amplifies super-horizon mode amplitudes by 1.45e+38 relative to vacuum evolution and produces a scale-invariant magnetic spectrum. Applied to a stated vacuum-scale seed, the output field at the turnaround carries an energy fraction 9.76e-13, safely below the backreaction ceiling and above the blazar floor's requirement, before any post-bounce processing. The contracting phase is long enough for coupling-driven generation to work without extreme exponents; that, quantitatively, is the opportunity a bounce offers magnetogenesis. Computed within a stated model, not measured.