Unified CPT-Symmetric Cyclic Cosmology: From Timeless Geometric Foundations to Relaxation-Driven Dynamics with Explicit Bounce Transfer

Relaxation-Driven Cyclic Cosmology ( RDCC ) 2.2 Unified CPT-Symmetric Cyclic Cosmology: From Timeless Geometric Foundations to Relaxation-Driven Dynamics with Explicit Bounce Transfer This is the updated version of the RDCC paper, now including an integrated Appendix on "Minimal RDCC Signature in Linear Structure Growth" with detailed derivations for Euclid-testable predictions. RDCC eliminates the following long-standing cosmological problems at once: initial singularity, need for inflation, cosmological constant problem, dark matter problem, dark energy problem, arrow of time, Tolman entropy problem, fine-tuning of initial conditions, baryon asymmetry, global preferred time direction, initial-value paradigm. RDCC solves them all without new fields, modified gravity or inflation. Relaxation-Driven Cyclic Cosmology (RDCC) is a minimal, nonsingular, eternally cyclic cosmological framework formulated entirely within standard Einstein gravity and a single complex scalar field. The theory is globally CPT-symmetric and fundamentally timeless: time, entropy production, and causal structure arise only as sectoral, thermodynamic projections of an underlying CPT-invariant spacetime. RDCC addresses a set of otherwise disconnected cosmological problems-dark energy, dark matter, baryon asymmetry, the arrow of time, the initial singularity, and entropy accumulation in cyclic models-by tracing them to a single structural assumption: the existence of a globally preferred time direction. By abandoning this assumption, RDCC replaces the standard initial-value paradigm with a CPT-symmetric cyclic attractor in which expanding and contracting phases are related by sectoral time reversal. Dark energy emerges as vacuum relaxation driven by a radiatively generated tilt in a double-well scalar potential, yielding an effective equation of state w > −1 without a cosmological constant. Dark matter corresponds to CPT-conjugate mirror-sector baryons that share the spacetime metric but possess an oppositely oriented thermodynamic arrow. A nonsingular cosmological bounce arises dynamically as a CPT fixpoint, while gravitationally mediated cross-sector relaxation prevents secular entropy growth and ensures multi-cycle stability without violating global entropy conservation. The framework requires neither inflation, modified gravity, nor additional degrees of freedom. RDCC yields concrete, falsifiable predictions, including characteristic gravitational-wave signatures, 21-cm modulations, deviations in ∆Neff, and a correlated resolution of late-time cosmological tensions. The theory is presented as a self-contained, testable alternative to ΛCDM. We develop a unified cosmological framework in which a timeless, globally CPT-symmetric geometric manifold provides the ultraviolet (UV) foundation for a two-sector effective cosmology at late times. The UV structure consists of a smooth two-dimensional manifold with a marginal critical line whose transverse instability generates two CPT-related sectors. Cosmological time, expansion, and contraction emerge as sectoral projections relative to this geometric structure, and the cosmological bounce corresponds to a CPT-symmetric fixpoint rather than a dynamical event in four-dimensional spacetime. A projection map from the geometric manifold to a four-dimensional Lorentzian spacetime yields an effective description in which the two sectors behave as gravitationally coupled fluids. At infrared (IR) scales this reduces to a minimal two-sector model with a single phenomenological relaxation parameter α. The background evolution is degenerate with ΛCDM, while linear perturbations exhibit a weakly damped isocurvature mode δI ∝a−α, leading to percent-level deviations in the growth rate fσ8(z) without affecting primary CMB anisotropies. The combined UV–IR framework provides a cyclic interpretation in which each sector represents one half of a CPT-symmetric cosmological cycle, and the bounce arises geometrically from the structure of the manifold. The model is minimal, internally consistent, and falsifiable with upcoming large-scale structure surveys such as Euclid, DESI, and CMB-S4. Related documents and the full RDCC ecosystem are available via Zenodo:https://zenodo.org/records/18204087 Michael Lehmannmi.lehmann@gmx.de