Relaxation-Driven Cyclic Cosmology (RDCC) + Companion Papers I, II, III, IV, V v2.0, VI, VII + Speculative Extensions

Relaxation-Driven Cyclic Cosmology (RDCC) v38.0 A fully predictive, one‑parameter cosmological framework RDCC v38.0 integrates two major advances into the framework: the full dynamical evolution of the relaxation parameter (Companion VI) and the complete linear perturbation theory including the Boltzmann hierarchy (Companion VII). With these additions, RDCC becomes a fully testable alternative to ΛCDM, ready for CLASS/CAMB implementation and future MCMC analyses. --- What’s New in v38.0 1. Companion VI: Dynamical Evolution of α(a)- Derivation of the evolution equation for the relaxation parameter α(a).- Demonstration of the freeze‑out at a ≈ 10⁻⁴, implying that all observable effects are governed by a single constant parameter α_IR.- Physical interpretation: relaxation generates the arrow of time, stabilizes the bounce, and couples the two sectors only through gravity and the dimension‑six operator. 2. Companion VII: Full Boltzmann Hierarchy- First complete RDCC formulation of linear perturbation theory.- Modified Einstein equations, coupled continuity and Euler equations, photon/neutrino hierarchies, mirror‑sector perturbations, and tensor‑mode modulation.- Fully implementable in CLASS/CAMB → RDCC is now numerically testable.- Log‑periodic tensor modulation provides a clear smoking‑gun signature for LISA, DECIGO, and the Einstein Telescope. 3. Structural and Consistency Improvements- Unified α‑notation across all Companions.- Precise definitions of all background quantities required for Boltzmann codes.- Harmonization and cleanup of the Companion series. --- Highlight from v37.0: Prototype Global Fit The Prototype Global Fit introduced in v37.0 remains a central achievement: - Best‑fit value: α_IR ≈ 0.016–0.018 - Consistent with: - n_s ≈ 0.965 - ΔN_eff ≈ 0.2–0.3 - a mild reduction in fσ₈ - a blue, modulated stochastic GW background - All deviations arise coherently from the same single parameter. While not yet a full MCMC analysis, the prototype fit demonstrates that RDCC is already competitive with ΛCDM at the predictive level and exhibits genuine explanatory power. --- *RDCC Flagship Paper & 8 Companions: *Companion I - FoundationsCPT‑symmetric global state, bipartite Hilbert space, mirror sector, bounce mechanism. *Companion II - Tensor Sector Log‑periodic modulation of gravitational waves; the key RDCC observational signature. *Companion III - Inter‑Sector Coupling Dimension‑six operator, temperature ratio x = T_-/T_+, origin of ΔN_eff. *Companion IV - Global CPT Structure Arrow of time, entropy, emergent causality. *Companion V - Observational Synthesis Prediction vector (n_s, ΔN_eff, fσ₈, Ω_GW), Prototype Global Fit. *Companion VI - Relaxation DynamicsEvolution equation for α(a), freeze‑out, one‑parameter nature of RDCC. *Companion VII - Boltzmann Hierarchy Complete linear perturbation theory, CLASS/CAMB‑ready implementation. *Speculative Extensions & Conceptual Companions II <-- (This document is not part of the predictive RDCC framework but a conceptual interpretation. The analogies do not validate RDCC, but demonstrate that its underlyingstructure is deeply rooted in known physics.) --- Summary RDCC v38.0 is the first version that is: - dynamically complete (α‑evolution),- perturbatively complete (Boltzmann system),- numerically testable (CLASS/CAMB‑ready),- empirically grounded (Prototype Global Fit),- and falsifiable (log‑periodic GW modulation). RDCC now stands as a fully developed, one‑parameter alternative to ΛCDM, ready for the next phase: MCMC likelihood analyses and gravitational‑wave forecasts. --- Cosmological Puzzles Addressed by RDCC RDCC provides unified structural explanations for several foundational problems: • Thermodynamic arrow of time: emerges as a sectoral property of a global CPT-symmetric state. • Initial singularity: resolved by a cuscuton-induced, ghost-free bounce. • Tolman entropy problem: avoided through global entropy conservation and minimal entropy at the bounce. • Dark matter: arises as a gravitational shadow of the CPT-conjugate sector, without new particle species. • Correlated deviations from ΛCDM: explained by the single relaxation parameter α. --- Related documents and the full RDCC ecosystem are available via Zenodo:https://zenodo.org/records/18204087 Michael [email protected]