A Predictive Two-Layer Fractal Cosmology

This paper presents an extended and methodologically explicit cosmological implementation of the Fractal Consistency Law (FCL), developed as a testable effective-cosmology benchmark rather than as a completed microscopic theory of quantum gravity. The model has a quantitatively specified two-layer structure. The first layer is a late-time fractal sector, controlled by the effective parameters ν0, α, and cs², which modifies the low-redshift expansion history and suppresses the growth of structure. The second layer is an early-time fractal-tension sector, parameterized by Ae and zc, which dynamically reduces the drag horizon rd and restores compatibility with compressed BAO indicators. The analysis is built from a compressed DES Y6 S8 target, compact BOSS DR12 fσ8 points, Pantheon+ supernova distances, and DESI DR2-inspired BAO ratios. A key result is the incorporation of an ex ante low-S8 prediction: before the final DES Year 6 result was released, the FCL dark-sector model had already selected S8 near 0.78 as the relevant low-clustering target. DES Y6 later reported S8 = 0.789 ± 0.012 in ΛCDM, placing the observational result very close to that prior prediction. The compressed FCL benchmark developed here finds a posterior-mean region around ν0 = 0.1650, α = 0.1319, Ae = 0.2105, zc = 2588, H0 = 73.76 km s−1 Mpc−1, rd = 136.69 Mpc, and S8 = 0.7893, with controlled contributions from the DES-inspired S8 target, BOSS growth, Pantheon+ distances, and compressed BAO. This should be read as a strong intermediate validation step rather than a final global fit: the current work still relies on compressed observables, a diagonal BAO approximation, and an S8 proxy rather than full covariance BAO, DES Y6 full 3x2pt, and CMB likelihoods. Nevertheless, it defines a coherent, falsifiable, and physically interpretable benchmark for the next phase of FCL cosmology.