Relaxation-Driven Cyclic Cosmology (RDCC) v35.0 + Companion Paper: Gravity as the Global Bridge in RDCC

Relaxation-Driven Cyclic Cosmology (RDCC) v35.0, represents the most complete and polished formulation of the framework to date. RDCC describes the Universe as a globally CPT-symmetric quantum state with a bipartite Hilbert-space structure, a Planck-suppressed inter-sector operator generating the universal relaxation parameter α ≈ 0.0175, and a cuscuton-induced nonsingular bounce connecting contraction and expansion. The theory predicts correlated deviations from ΛCDM, including a nearly scale-invariant scalar spectrum, a blue-tilted stochastic gravitational-wave background, and distinctive log-periodic tensor oscillations arising from CPT-induced interference between the two sectors. New in v35.0:• Fully restructured and professionally refined manuscript, including a reorganized Section 6 on perturbations and tensor phenomenology. • Introduction of a clean two-panel figure illustrating the RDCC log-periodic modulation: (i) the subtle physical modulation in the observational k-range, and (ii) the full oscillatory structure over an extended logarithmic domain. • Improved analytical treatment of the log-periodic tensor signature, including explicit expressions for the modulation amplitude, phase, and log-period. • Clarified derivation of the effective Newton constant \(Geff = G_N / (1 + ρ_-/ρ_+)\) and its interpretation as the gravitational shadow of the mirror sector. • Refined presentation of the bounce conditions, the role of α → 0 at the CPT-symmetric point, and the stability of the nonsingular turnaround. • Enhanced consistency across notation, equations, and figure references throughout the manuscript. • Integration of insights from the companion paper "Gravity as the Global Bridge in RDCC", strengthening the conceptual and mathematical foundations of the global two-sector structure. RDCC v35.0 is the flagship reference version of the framework, consolidating its conceptual foundations, effective field theory structure, bounce dynamics, perturbation theory, and observational predictions. This release provides a stable baseline for future companion papers and subsequent iterations of the theory. ------------------------------------------------------------------- Companion Paper I: Gravity as the Global Bridge in RDCC The companion paper provides the formal mathematical foundation underlying RDCC. It develops the structural role of gravity in a bipartite CPT-symmetric Universe and derives the key equations used in v35.0. Highlights include: • Variation of the global Einstein–Hilbert action in a two-sector Hilbert space. • Derivation of the effective Newton constant Geff = GN / (1 + ρ– / ρ+), explaining the apparent weakness of gravity. • Definition of the gravitational shadow of the mirror sector as the structural origin of dark matter. • Two-sector stress-energy dynamics and the relaxation operator T(+) T(–) / M*². • Linearized tensor equations and CPT-induced correlations, including the origin of log-periodic gravitational-wave modulations. • Bounce fixpoint and global CPT symmetry as structural boundary conditions. This companion paper is not an add-on but a formal backbone: it shows why gravity is the unique global interaction and how the RDCC structure emerges from first principles. --------------------------------------------------------------------- The document “RDCC – Speculative Extensions & Conceptual Companions”, is a purely conceptual and interpretative companion to the main framework. It explores structural analogies (e.g. to condensed-matter systems, holography, black-hole interiors and the problem of time) and philosophical implications of the global CPT-symmetric structure without introducing any new fields, mechanisms, parameters or observational predictions. It does not alter the core predictive model of RDCC v35.0 in any way. --------------------------------------------------------------------- Relationship between the three documents: • RDCC v35.0 presents the complete, predictive core framework. • The companion paper “Gravity as the Global Bridge” shows why the framework works mathematically. • The RDCC – Speculative Extensions & Conceptual Companions document offers conceptual and interpretative companions to RDCC. It explores structural analogies and philosophical perspectives without modifying the core dynamics, introducing new predictions, or altering any observable consequences of the model. Related documents and the full RDCC ecosystem are available via Zenodo:https://zenodo.org/records/18204087 Michael Lehmannmi.lehmann@gmx.de