CPQ Theory: CMB Spectral Index from Chiral Topology of the Matrix

Within CPQ theory, we propose that the spectral index of primordial fluctuations n_s can be linked to the chiral correction of the distribution of topological loops formed during the early phase transition. In this picture, the approximately scale-invariant critical loop network leads to n_s ≈ 1, while a nonzero chiral order parameter Ξ_0 generates a small red tilt. For an effective number of degrees of freedom Ndof = 4 (three compressive + one torsional), we obtain the relation n_s = 1 - Ξ_0^2/4, which for Ξ_0 ≈ 0.37 gives a value consistent with the observed CMB spectrum (Planck: n_s = 0.9649 ± 0.0042, agreement within 0.4σ). The article identifies where in the chain the steps are derived, where they are structural arguments, and where they are open bridges. Key prediction: the factor 1/4 is a geometric constant of the three-dimensional matrix, and the value of Ξ_0 is independently measurable from galaxy rotations and cosmic birefringence. Porschová, A. (2026). CPQ Theory — A Unified Framework from Spacetime Quanta to Cosmology (Books I–III). Zenodo. https://doi.org/10.5281/zenodo.18686137 Porschová, A. (2026). CPQ Field Theory — Applications (Books 01–03). Zenodo. https://doi.org/10.5281/zenodo.19100819 Porschová, A. (2026). The Matrix — Parameters and Dynamics: Foundation of CPQ Theory (3.1). Zenodo. https://doi.org/10.5281/zenodo.19431867