Relaxation-Driven Cyclic Cosmology (RDCC) v50.0

Relaxation-Driven Cyclic Cosmology (RDCC) v50.0 Ten self-contained papers presenting a bipartite, CPT-symmetric cosmological framework. This version marks the completion of the framework's theoretical development and includes numerical corrections to v49.0. What this version is, and what it is not RDCC describes the Universe as a single quantum state, exactly symmetric under the combined operation of charge conjugation, parity, and time reversal. Realizing that symmetry requires two sectors, a visible one and an exact conjugate, sharing one spacetime geometry and interacting only through gravity and through the gradual loss of quantum coherence between them. A smooth bounce replaces the initial singularity. The thermodynamic arrow of time emerges when a single observer, confined to one sector, is forced to describe their half of an entangled whole. This is not presented as a finished cosmology. It is a coherent theoretical framework with a single sharp falsification condition, stated below, and with several structural results that stand independently of whether the framework as a whole is confirmed. The theoretical development is complete in the sense that the framework's internal consequences have been worked out; further progress now depends on observation rather than on additional theory. Corrections to v49.0 Two numerical errors in v49.0 were found during subsequent work and are corrected here. Both are numerical rather than conceptual, and no structural conclusion changes, but anyone working from the v49.0 numbers should replace them. First, the effective number of relativistic species was normalized to the total radiation density rather than to the photon density. The standard definition uses the photon density, and the mirror sector contributes both photons and neutrinos, so a factor accounting for the mirror sector's full relativistic content was missing. The numerical prefactor is 7.404, not 4.403. Second, the sectoral temperature ratio was quoted as 0.27 where the correct value following from the coupling asymmetry is 0.361. The corrected values are: coupling asymmetry minus 0.967, sectoral temperature ratio 0.361, effective gravitational coupling enhanced by 1.7 percent rather than 0.53 percent, mirror baryons at 4.7 percent of the visible baryon density rather than 2 percent, and the shortfall of thermal mirror matter relative to the observed dark matter density a factor of 116 rather than 278. The structural conclusion that thermal mirror matter cannot be the dark matter is unchanged, since a shortfall of two orders of magnitude remains. The framework in outline The relaxation between the two sectors is not modelled by an assumed rate equation. Treating the visible sector as an open quantum system with the mirror sector as its environment, a theorem guarantees that any physically admissible description must take the Lindblad form, and the physical requirements of the framework then determine the coupling structure essentially uniquely. Two structurally distinct relaxation rates follow, related by the standard factor of two between coherence and population relaxation, and the coherence order parameter turns out to be a derived function approaching complete decoherence rather than a free constant. Dark matter is a superheavy, collisionless species produced gravitationally by the bounce, with abundance fixed by the bounce curvature scale and independent of sectoral thermodynamics. The relevant quantum coefficients are computed explicitly rather than estimated. Three parameters govern the framework, each determined by a distinct observational channel. Two of them stand in one to one correspondence with quantities already free in standard cosmology, the spectral index and the cold dark matter density, so they are reparametrizations rather than additions. Relative to the standard model, the framework adds exactly one parameter. The falsification condition The framework makes one prediction that is distinguishable from standard cosmology and testable with foreseeable instruments: The growth rate of cosmic structure is suppressed by 1.40 percent, with an uncertainty of 0.17 percent. The coefficient in this relation is derived, not fitted, and the parameter entering it is already fixed by the measured spectral index. Current growth rate measurements have uncertainties of five to ten percent, so this prediction is below present sensitivity. Surveys now underway are expected to reach the required precision. A measured suppression inconsistent with this value falsifies the relaxation sector of the framework. The framework's other distinctive predictions are not currently testable. The relic gravitational wave background generated at the bounce has a definite predicted frequency of about 0.8 megahertz, but a predicted amplitude some fifteen orders of magnitude below any current or proposed detector. The dark energy equation of state is predicted to be exactly minus one with no perturbations at any wavelength, which is not distinguishable from a cosmological constant. A predicted break in the primordial spectrum at the matter radiation equality scale lies within cosmic variance. We state this plainly: in its present form the framework is empirically distinguishable from standard cosmology through one measurement. Two results that stand independently Two findings in this release do not depend on the correctness of the framework as a whole and may be of interest on their own terms. The open quantum system treatment of inter-sector decoherence. That cosmological decoherence between two sectors satisfies the standard relation between coherence and population relaxation times, that a Hermitian coupling operator provably cannot relax the observable it is built from, and that the coherence order parameter cannot be a free parameter of such a construction, are results about open quantum systems in cosmology rather than about this particular cosmology. A no go result for mirror matter as dark matter. The dark radiation constraint scales as the fourth power of the sectoral temperature ratio while the mirror matter abundance scales as the third power, and satisfying either violates the other by two orders of magnitude. Independently, a relational interpretation in which each sector sees the other as its dark matter would require two observers to measure reciprocal values that cannot both match observation. Together these exclude an entire class of models, not only the variant considered here. What the framework does not address The magnitude of the dark energy density is not explained. It is located in the late time potential of the field that drives the bounce, which yields an exactly constant equation of state and the absence of dark energy perturbations, but the value itself remains a free parameter with the same status the cosmological constant has in standard cosmology. The baryon asymmetry is not derived. A baryon number violating coupling is admissible within the framework, but it introduces a further free parameter fixed by one observable and tested by none, which worsens rather than improves the accounting. The suppression of anisotropy growth during the contracting phase, a generic difficulty for bouncing cosmologies, is not established here. The added parameter of the framework is currently fixed by a single observational channel and tested by none. Three approaches to providing a second channel were examined during this work and none succeeded, for reasons documented in full. The ten papers Entry point. Relaxation-Driven Cyclic Cosmology, the complete architecture, citing each result to the paper that establishes it. Foundations. The Lindblad Mechanism and Gravity as the Global Bridge. The relaxation sector. Relaxation Rates and Freeze-Out, including the derivations of the spectral tilt and the growth rate suppression. The bounce. The Cosmological Bounce. Applications. Dark Matter from Gravitational Particle Production at the Bounce, Sectoral Thermodynamics, Sectoral Perturbation Equations and Structure Formation, and Dark Energy: A Structural Placement, Not an Explanation. Observations. Numerical Fits. A note on method Every quantitative claim was checked by explicit computation before being written down, using symbolic algebra for the operator results, numerical integration for the particle production coefficients, and posterior sampling for the parameter determination. Where a check failed the claim was withdrawn rather than reworded, and several mechanisms examined during this work are absent from the release for that reason. Where a result could not be obtained the papers say so instead of supplying a plausible looking substitute. Limitations are stated in the same sections as the results they qualify. Michael Lehmann 79730 Murg/Germanymi.lehmann@gmx.de