Cosmic Birefringence from Non-Orientable Spacetime Topology: Scenario, Prediction, and Observational Tests

Recent analyses of Cosmic Microwave Background (CMB) polarization from Planck, WMAP, and the Atacama Cosmology Telescope (ACT DR6) report evidence for isotropic cosmic birefringence β ~ 0.2^∘ - 0.35^∘. We propose a scenario where cosmic birefringence arises from a $CPT$-symmetric cosmological bounce modeled as a non-orientable four-dimensional spacetime quotient M₄ = (R × S³)/Z₂. Integrating out Standard Model fermions in this non-trivial Pin⁺(3,1) bundle induces a global spectral asymmetry governed by the Atiyah--Patodi--Singer η-invariant on the spatial section RP³. Using Peter--Weyl decomposition and Hurwitz zeta regularization, we evaluate η(D) = 1/4. Via the canonical Dai--Freed boundary phase ΦDF = (π/2)η(D) = π/8 and exact 1-loop Chern--Simons matching, under the phase-matching ansatz Δθ₅ = ΦDF, the theory predicts a canonical birefringence angle |β|canon = 1/2|θvac| = αₑₘ/2 ≈ 0.2091^∘ (with an alternative direct phase map predicting |β|ₐₗₜ = αₑₘ ≈ 0.4181^∘). The canonical prediction agrees with ACT DR6 (β = 0.215^∘ ± 0.074^∘, pull -0.08σ) and the global weighted mean (β = 0.264^∘ ± 0.058^∘, pull -0.95σ). In the expanding background, tight Thomson scattering before recombination randomizes polarization while Hubble friction locks the scalar condensate at χ ≈ 0; coherent birefringence accumulates during transparent free-streaming, while local Galactic dust is unrotated (βdust ≈ 0). First-principles integration on RP³ proves strict scale invariance (β_ = const) for R₀ ≥ 15.8 \, c/H₀. Realistic Fisher forecasts demonstrate that LiteBIRD and Simons Observatory will detect αₑₘ/2 at > 11.6σ and separate it from αₑₘ at 11.6σ, providing a quantitative empirical test of spacetime topology.