Log-Periodic Cosmology from Complex Scaling Symmetry

We construct a covariant scalar-field cosmology derived from universal properties of discrete scale invariance (DSI) and complex scaling exponents, motivated by oscillatory structures appearing in analytic number theory. When a system exhibits complex scaling symmetry with exponent λₙ = −γ + iω its observables acquire log-periodic corrections of the form a⁻γ cos(ω ln a). We apply this structure to a canonical scalar-field cosmology, producing an exponentially damped oscillatory potential and a late-time attractor solution that asymptotically recovers ΛCDM. The model generates correlated oscillations in H(z), fσ8(z), and P(k), all periodic in ln a. A full empirical pipeline is provided for implementation in CLASS/CAMB and Bayesian inference frameworks including Cobaya and MontePython