R-layer Mode Theory (RLMT) L: Cosmological Dynamics of Tension Fields and the Growth of Supermassive Black Holes

This volume develops the cosmological extension of the R-layer Mode Theory (RLMT) by introducing the tension field σ(ξ,t) and its anisotropic component Δσ ≡ Ao as the fundamental drivers of SMBH growth, galaxy formation, and cosmic evolution. By extending the Mode Tension Field Equation (MTFE) to an FRW background, we derive the cosmological dynamics of tension fields and show how their fluctuations regulate accretion, jet launching, recoil forces, and feedback. Recent observations of Cygnus X‑1—including instantaneous jet‑power measurements and wind‑induced jet bending—provide empirical calibration for Ao and validate its role in anisotropic energy‑momentum transport. The volume presents observational predictions for LSST, Roman, and SKA, including SMBH seed mass functions, high‑z SMBH abundance, galaxy‑shape statistics, reprojection events, and kick‑velocity distributions. This work establishes the cosmological completion of the R-layer Mode Theory.