Quantitative Analysis of Cosmic Vorticity as a Source of the NANOGrav Gravitational Wave Background.

We present a quantitative connection between cosmic vorticity detected in DESI data and the gravitational wave background observed by NANOGrav. The measured vorticity parametersspectral index nω = −1.266, amplitude Aω = 3.10 × 10^9 , and double evolu- tionary scale (γH0 = 4.47, γS8 = 1.65)naturally map onto an ultralight axion eld with mass ma = 1.8 × 10^−22 eV. We derive explicit formulas connecting vorticity to axion pa- rameters, predicting a gravitational wave background with ΩGW = (3.15 ± 0.53) × 10^−9 and spectral index γ = 4.53, in remarkable agreement with NANOGrav's measurement of ΩGW = (2.4 ± 0.7) × 10^−9 and γ = 13/3 ≈ 4.33. This unied framework simultaneously re- solves the H0 and S8 tensions while providing a testable dark matter candidate, establishing cosmic vorticity as a bridge between quantum gravity and observational cosmology.