Relaxation-Driven Cyclic Cosmology (RDCC) + Companions I - X + One Speculative Extensions

Relaxation-Driven Cyclic Cosmology (RDCC) v40. 0 What's new in v40. 0 Version 40. 0 marks a major theoretical milestone for the RDCC framework. While previous versions introduced the relaxation rate Γ = αH phenomenologically, v40. 0 provides the first rigorous microscopic derivation of this linear-in-H law. Companion IX (NEW), introduces the RDCC Consistency Triangle, showing that Γ ∝ H emerges naturally from three independent structural pillars: bipartite entanglement flow, scaling of the dimension-six inter-sector operator, and the emergent coherence boundary. Companion X (NEW), provides the first full microscopic derivation using a Born–Markov master equation and Lindblad-type evolution in an expanding FRW background. The resulting relaxation rate Γ ∝ H emerges directly from the scaling of stress-tensor correlators and Hubble-scale coarse-graining, without heuristic assumptions. These additions significantly strengthen the theoretical foundation of the relaxation dynamics central to RDCC. --- 3. Fully Integrated RDCC EcosystemRDCC v40. 0 includes: - Flagship Paper - Companion I - Companion II - Companion III - Companion IV- Companion V (v2. 0) - Companion VI - Companion VII - Companion VIII - Companion IX (new) - Companion X (new) - Speculative Extensions - Conceptual Companions II <-- This document is not part of the predictive RDCC framework but a conceptual interpretation! (These analogies do not validate RDCC, but demonstrate that its underlying structure is deeply rooted in known physics. ) --- Key puzzles solved by RDCC • The thermodynamic arrow of time: Time and entropy increase are emergent phenomena resulting from the projection of a globally timeless, CPT-symmetric bipartite quantum state onto a single sector. • The cosmological singularity: Replaced by a nonsingular bounce at the CPT fixed point of the global state. • The Tolman low-entropy problem: Global entropy reaches a minimum at the bounce; the apparently low entropy of our sector is a consequence of sectoral projection. • The origin and nature of dark matter: Pure gravitational shadow of the CPT-conjugate mirror sector, interacting only gravitationally. • The apparent weakness of gravity: Effective Newton constant measured by sectoral observers is Geff = GN / (1 + ρ−/ρ+). • Correlated small deviations from ΛCDM: Scalar spectral tilt (nₛ−1 = −2αIR), dark radiation excess (ΔNₑff ∼ αIR), percent-level growth-rate shift in fσ8, and log-periodic modulation in the stochastic gravitational-wave background - all governed by a single parameter αIR. • The origin of the invariant speed of light c: Emergent inter-sector coherence boundary, the maximum speed at which global quantum coherence can propagate before relaxation enforces decoherence. • The cyclic structure of the Universe: Natural consequence of imposing global CPT symmetry on the full cosmological quantum state. RDCC solves these long-standing puzzles through a single structural postulate - global CPT symmetry of the complete quantum state in a bipartite Hilbert space - together with the minimal dimension-six inter-sector operator. The framework remains highly predictive with only one free parameter. --- Related documents and the development history of the RDCC framework are available on Zenodo: https: //zenodo. org/records/18204087 Michael Lehmannmi. lehmann@gmx. de