R-layer Mode Theory V: Cosmic Asymmetry and Domain Wall Cosmology

This Volume V develops the cosmological sector of the R-layer Mode Theory (RLMT) by introducing a single mode field ϕ that acts as an order parameter for the local state of the higher-dimensional R-layer. The field is governed by a double-well potential and a tension-induced non-minimal coupling ξ(ϕ)R, which together determine cosmic asymmetry, vacuum selection, and the formation of AUP/MUP domains. Curvature in the early universe tilts the effective potential Veff(ϕ)=V(ϕ)+ξ(ϕ)R, selecting a preferred vacuum and generating an initial global asymmetry. As curvature decreases, spatial fluctuations allow different regions to fall into opposite vacua, producing a network of AUP/MUP domain walls. These walls behave as gravitationally active membranes whose tension, curvature response, and internal fluctuation spectrum influence matter on galactic and cosmological scales. We derive the gravitational field of a wall, its effective stress-energy tensor, and show that wall-induced accelerations naturally produce MOND-like phenomenology without invoking dark matter. On cosmological scales, the domain wall network provides a geometric origin for the filament–void structure of the cosmic web, with filaments forming at wall intersections and voids arising from wall repulsion. Fluctuations on the wall satisfy a Schrödinger-type equation, supporting a translational zero mode and massive bound states that encode localized distortions of the R-layer geometry. These modes determine how information and energy propagate along the wall and contribute to the dynamics of large-scale structure. Together with Volumes 0–IV, this work establishes the R-layer Mode Theory as a unified geometric framework for cosmic asymmetry, domain formation, and large-scale cosmology.