R-layer Mode Theory (RLMT) XCIV: Layer Transition Cosmology and Early‑Universe Hierarchy Evolution

This volume develops a mathematically precise and physically motivated framework for Layer Transition Cosmology within R-layer Mode Theory (RLMT). As stated in the manuscript, “the early universe is described by a high-density AUP/MUP regime (hierarchy theory A) in which layers are effectively unseparated and the force hierarchy is not yet emergent.” We introduce a local AUP/MUP density PAUP/MUP(x,t), define hierarchy regions A/B/C via density thresholds, and construct an inhomogeneous phase-transition picture in which hierarchy fronts propagate through spacetime. These transitions synchronize with the emergence of the force hierarchy, multipole stabilization, and the separation of layers. A collapse probability functional Pcollapse(x,t) is introduced to model toy primordial-black-hole (PBH) formation rates and galaxy-seed distributions in hierarchy B. The formalism integrates naturally with the dynamic layer geometry of RLMT XCIII, including time-dependent tension fields, observer-dependent kernels, and effective tensor fields. This framework provides a rigorous basis for interpreting early-universe signatures—PBHs, early galaxies, gravitational waves, and CMB anisotropies—in terms of RLMT hierarchy evolution. It establishes RLMT as a hierarchy-evolution cosmology in which the universe transitions through spatially inhomogeneous A/B/C regimes rather than evolving uniformly.