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

Within CPQ theory, we propose that the spectral index of primordial fluctuations nₛ 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 nₛ 1, while a nonzero chiral order parameter ₀ generates a small red tilt. For an effective number of degrees of freedom N₃₎₅ = 4 (three compressive + one torsional), we obtain the relation nₛ = 1 - ₀²/4, which for ₀ 0. 37 gives a value consistent with the observed CMB spectrum (Planck: nₛ = 0. 9649 0. 0042, agreement within 0. 4). 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 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