Relaxation-Driven Cyclic Cosmology (RDCC) v43.0: Flagship Paper + 20 Companions + 1 Companion/Numerical Fits

Relaxation-Driven Cyclic Cosmology (RDCC) v43.0, April 24, 2026 This is the current and recommended version of the RDCC framework. It contains:• the Flagship Paper (submitted to journal)• Companions I–XX (foundational papers)• Companion “Numerical Fits” (new numerical constraints on the single parameter α using χ², MCMC, RSD and Fisher forecast) Note for referees: The submitted manuscript refers to the previous Zenodo record v41.0. All content of v41.0 is fully included in this version v43.0, which additionally provides the new numerical Fits Companion + new Companions XII - XX. Referees are kindly invited to consult the latest version v43.0 for the most up-to-date material. New in RDCC V43.0: (Companions XVI–XX) This release adds the final core Companions XVI through XX to the Relaxation-Driven Cyclic Cosmology (RDCC) series, bringing the framework to full computational and phenomenological maturity. Companion XVI – The RDCC Boltzmann Code Presents the complete numerical framework: modified Friedmann equations with sectoral energy exchange, relaxation-corrected scalar/vector/tensor perturbation equations, and a fully generalized Boltzmann hierarchy for photons, neutrinos, baryons and the mirror sector. Provides a CLASS/CAMB-compatible blueprint with initial conditions and parameter mappings - the computational backbone for all future RDCC predictions. Companion XVII – Cosmic Magnetic Fields Introduces a new, universal magnetogenesis mechanism driven by inter-sectoral decoherence gradients. Anisotropic stress fluctuations generated during the relaxation-dominated epoch act as a source term in the Maxwell–Einstein system, producing coherent magnetic seed fields with naturally large correlation lengths - without new fields or explicit symmetry breaking. Companion XVIII – Small-Scale Structure Derives the scale-dependent growth function D(a,k) arising from sectoral sound-speed differences, free-streaming lengths and relaxation-induced damping. Predicts characteristic suppression of power on scales k ≳ k_rel together with enhanced vorticity - directly addressing the S8 tension, Lyman-α forest slope and small-scale clustering observables. Companion XIX – Non-Linear Structure Formation Extends linear results to the non-linear regime. Provides relaxation-modified spherical and ellipsoidal collapse thresholds, an adjusted Press–Schechter/Sheth–Tormen halo mass function, and a modified concentration–mass relation. Introduces a relaxation-adjusted halo model for the non-linear matter power spectrum and cosmic-web morphology. Companion XX – Baryonic Physics and Feedback Develops the full baryon sector within RDCC. Shows how relaxation-delayed collapse, reduced virial temperatures and vorticity reshape gas cooling, star-formation efficiency, supernova/AGN feedback and baryon redistribution. Constructs an RDCC-adjusted baryonic correction model (RDCC-BCM) and derives its impact on X-ray, SZ, HI and galaxy-formation observables. --- Together these Companions close the remaining major gaps in the RDCC program: they provide a ready-to-use numerical implementation, extend the framework into small-scale/non-linear structure formation, cosmic magnetogenesis and baryonic astrophysics, and deliver a rich set of correlated, falsifiable predictions across CMB, large-scale structure, gravitational waves, magnetic fields and galaxy surveys. Fully Integrated RDCC EcosystemRDCC v43.0 includes: RDCC Flagship Paper - Companion I Gravity as the Global Bridge- Companion II Tensor Interference and Log-Periodic Gravitational Waves- Companion III Relaxation Dynamics and the Scalar Sector- Companion IV The Global CPT State and the Mirror Sector- Companion V Observational Synthesis and Global Fit- Companion VI Dynamical Generation of the Relaxation Parameter- Companion VII Boltzmann Hierarchy and Linear Perturbations- Companion VIII Emergent Speed of Light as an Inter-Sector Coherence Boundary- Companion IX Derivation of the Relaxation Rate- Companion X Microscopic Derivation of the RDCC Relaxation Rate from the Dimension-Six Inter-Sector Operator- Companion XI Dark Energy as Emergent Relaxation Dynamics- Companion XII Sectoral Baryon Asymmetry from Opposite Thermodynamic Arrows- Companion XIII The Neutrino Sector in the Relaxation-Driven Cyclic Cosmology Mass Hierarchy- Companion XIV Primordial Black Holes in the Relaxation-Driven Cyclic Cosmology Relaxation-Suppressed Collapse- Companion XV The Early-Universe Gravitational-Wave Spectrum - Companion XVI The RDCC Boltzmann Code - Companion XVII Cosmic Magnetic Fields - Companion XVIII Small-Scale Structure - Companion XIX Non-Linear Structure Formation - Companion XX Baryonic Physics and Feedback - Companion: Numerical Fits and Observational Constraints on the Relaxation Parameter α in RDCC - 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 (n_s − 1 = −2 α_IR), dark radiation excess (ΔN_eff ∼ α_IR), percent-level growth-rate shift in fσ8, and log-periodic modulation in the stochastic gravitational-wave background - all governed by a single parameter α_IR. • 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. • The late-time cosmic acceleration: Emergent from the same relaxation dynamics that govern early-universe predictions; the freeze-out of the coherence parameter α(a) naturally produces an effective acceleration term without invoking a cosmological constant or new fields. 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