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 αIR. - 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: αIR ≈ 0. 016–0. 018 - Consistent with: - nₛ ≈ 0. 965 - ΔNₑff ≈ 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 the key RDCC observational signature. *Companion III - Inter‑Sector Coupling Dimension‑six operator, temperature ratio x = T_-/T_+, origin of ΔNₑff. *Companion IV - Global CPT Structure Arrow of time, entropy, emergent causality. *Companion V - Observational Synthesis Prediction vector (nₛ, ΔNₑff, fσ₈, ΩGW), 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 Lehmannmi. lehmann@gmx. de
Michael Lehmann (Fri,) studied this question.