Quantum-Cosmo Unification via Radion Modulation in Fractal Inflationary Branes and Entropic Flux Conservation in Boundary Singularities

Abstract

We propose a unified quantum and relativistic model based on a fractal multiverse topology, wherein local spacetime is embedded as a 3-brane within an eleven-dimensional bulk hyperspace. We demonstrate that the cosmological constant (Λ) is induced by an inter-brane dilaton and graviscalar field (Φ) generated by the dielectric friction of contiguous membranes arranged in a self-similar fractal foam geometry. To avoid ghost fields and tachyons, the dilaton potential is constrained via stable inflationary slow-roll conditions. Furthermore, we introduce the principle of pyramidal conservation, postulating that black hole singularities are not absolute information sinks but rather metric transducers that pump compressed mass-energy through the six compactified dimensions of Calabi-Yau spaces via the ER=EPR conjecture and fuzzball theory, governed by the Page curve. To guarantee the falsifiability of the model, an Astrophysical Verification Appendix is attached, predicting a quantum phase micro-delay in Hawking radiation and geometric polarization anomalies in the Cosmic Microwave Background (CMB), detectable through next-generation instrumentation.