Taijitu Relaxation Cosmology: Sharp Forecasts for Euclid Weak Lensing and SKA 21-cm Observations

This work extends Lehmann (2025), Zenodo DOI:10.5281/zenodo.17680370 The Taijitu Relaxation Cosmology is a minimal cyclic model that explains the DESI 2024 hints of evolving dark energy with exactly one additional physical parameter. It is based on a nearly degenerate scalar double-well potential V(φ) = λ(φ² − v²)² + εφ + δ (ε, δ ∼ 10⁻¹²⁰ M_Pl⁴). In the matter-dominated era, stochastic Starobinsky–Yokoyama relaxation drives the occupation probability of the deeper minimum as P⁻(a) ≈ C · a³ ln(a/a₀) with C ≈ 9.4·10⁻¹¹. This yields a dynamical dark energy ρ_DE ∝ a³ ln a with equation of state w(a) = –1 + 1/(3 ln a + const). Present-day values are w₀ ≈ –0.9968 ± 0.0018 and w_a ≈ –0.82, lying well inside the 1σ contour of DESI 2024 + Pantheon+ data (Δχ² ≈ –2.7 relative to Planck-ΛCDM). The model is globally CPT-symmetric, singularity-free, cyclic (period ≈ 100 Gyr), and simultaneously resolves the cosmological coincidence problem, the Hubble tension (H₀ = 68.9 ± 1.1 km s⁻¹ Mpc⁻¹), and the origin of the arrow of time. Three sharp predictions are: +11.8 % ISW excess (Euclid×CMB-S4), 0.28 % oscillation in the 21-cm power spectrum (SKA Phase 2), and w(z=0.3) = –1.003 ± 0.005 by 2035.