Relaxation-Driven Cyclic Cosmology (RDCC) v5.0: Bounce-Matching Formalism, Mirror-Sector Dynamics, and Refined Gravitational Waves

Relaxation-Driven Cyclic Cosmology (RDCC) is a nonsingular, eternally cyclic cosmological model based on a single effective complex scalar order-parameter field Φ evolving in a tilted double-well potential. The tilt emerges from radiative Coleman–Weinberg corrections, requiring no ad-hoc parameters. Field relaxation drives time-varying vacuum energy, generating alternating phases of accelerated expansion and contraction in an eternal "breathing" cycle. A gravitationally coupled CPT-conjugate mirror sector with reversed thermodynamic arrow provides cold dark matter and resolves baryon asymmetry via phase-induced mechanisms, preserving global CPT symmetry exactly. The model operates as an effective field theory on cosmological scales, avoiding singularities, entropy divergence, flatness problems, and the need for inflation or modified gravity. Key predictions include ~12% excess in low-ℓ CMB Integrated Sachs–Wolfe effect, primordial perturbations from the bounce (n_s ≈ 0.964, A_s ≈ 2.1×10^{-9}, Planck-kompatibel), peaked GW spectrum (~5 mHz, Ω_GW h² ~10^{-10}–5×10^{-9}, LISA-testbar), small-scale suppression, and 21-cm modulations. v5.0 upgrades:- Formal CPT-symmetric bounce-matching for scalar/tensor perturbations (preserves scale-invariance, introduces tensor knick structure).- Dynamic mirror-sector evolution (temperature T_-, decoupling, ΔN_eff < 0.1, quantitative DM/baryon ratio derivation).- Refined GW spectrum (broken power law with plateau and bounce signatures). Aligns with DESI DR2 hints of evolving dark energy (e.g., w_0 > -1, w_a < 0; arXiv:2508.17955, 2504.15222). Testable with LISA/PTA (GW knick), Euclid BAO (ΔN_eff, structure growth), SKA/HERA (21-cm), JWST (small-scale), LHC (Higgs). Falsifiability: No mHz GW peak/knick (LISA/PTA), no ISW excess (Euclid/CMB experiments), ΔN_eff > 0.1 (BBN/CMB), incorrect η_B or Ω_DM/Ω_b. Full LaTeX source and code in Appendix. Builds on v4.0 (Zenodo 10.5281/zenodo.18304744) and v3.0 (10.5281/zenodo.18281686). While the core of RDCC remains a structural, timeless framework with fixpoint character, this document explores a dynamical realization of the bounce mechanism to enable concrete, falsifiable predictions. Related documents and the full RDCC ecosystem are available via Zenodo:https://zenodo.org/records/18204087 Michael [email protected]