(v41.0) Relaxation-Driven Cyclic Cosmology (RDCC) + Companions I - XI + One Speculative Extensions

Relaxation-Driven Cyclic Cosmology (RDCC) v41.0, 

presents the complete and most coherent formulation of the framework to date. This release includes the flagship paper, Companions I–XI, and the Speculative Extensions document, providing a unified and self-consistent description of RDCC as a CPT-symmetric, bipartite cosmological model with emergent classical spacetime, Hubble-driven decoherence, and relaxation-induced phenomenology.

New in v41.0:

Companion XI - Dark Energy as Emergent Relaxation Dynamics in Relaxation-Driven Cyclic Cosmology (RDCC)

The only addition in this version is Companion XI, which introduces a structural reinterpretation of cosmic acceleration within the RDCC framework. Building on the microscopic relaxation dynamics derived in Companion X, Companion XI shows that the suppression and late-time freeze-out of the inter-sector coherence parameter α(a) naturally generate an effective acceleration term in the coarse-grained Friedmann equations. This mechanism reproduces the observational signatures of dark energy without introducing a cosmological constant or any new fundamental field.

Companion XI demonstrates that the onset of acceleration coincides with the freeze-out of α(a), resolving the “Why now?” problem as a dynamical consequence of the proportionality Γ(a) ∝ H(a) and the Hubble-scale memory time. The resulting effective dark-energy behaviour is emergent, dynamical, and structurally tied to the same relaxation process that governs the early-universe predictions of RDCC.

   A single mechanism explains:
• the emergence of classical spacetime,  
• the nearly scale-invariant scalar spectrum,  
• the blue-tilted stochastic gravitational-wave background,  
• the log-periodic tensor modulation,  
• the predictions for the scalar spectral index (nₛ), the effective number of relativistic species (ΔN_eff), and the growth-rate observable fσ₈,
• and now, the late-time cosmic acceleration.  

No new fields, no additional parameters, and no cosmological constant are required.  
Companion XI completes the conceptual arc of RDCC by showing that dark energy is not a separate component but an emergent consequence of the same relaxation dynamics that shape the entire cosmological evolution.

RDCC v41.0 therefore represents the first fully unified version of the framework, consolidating its early- and late-time predictions into a single coherent mechanism.

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3. Fully Integrated RDCC Ecosystem
RDCC v41.0 includes:

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 (v2.0)   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 (NEW!)  Dark Energy as Emergent Relaxation Dynamics

- 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.)

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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.

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Related documents and the development history of the RDCC framework are available on Zenodo:
https://zenodo.org/records/18204087

Michael Lehmann
mi.lehmann@gmx.de