We present the formal cosmological resolution of the Lyman-alpha (\ Lyman-) forest tension within the Guerrero self-interacting Fuzzy Dark Matter (si-FDM) framework. Standard non-interacting FDM models suffer from a fundamental paradox: the low boson mass required to solve small-scale galactic core challenges (m₂₂ 1–8) severely underpredicts the power spectrum of the high-redshift intergalactic medium, violating observational constraints that enforce m₂₂ > 20 (Iršič et al. 2017). By implementing the non-linear attractive self-interaction coupling (g₍₋ = 0. 00597) derived deterministically from the infrared fixed point of the renormalization group flow (Paper 2, ₈ₑ = 0. 5094), we compute the corrected cosmological matter transfer function T ₒ₈ (k). The attractive term provides an effective structural rigidity that shifts the half-power suppression scale from k₁/₂ = 12. 8 Mpc^-1 (free FDM) to k₁/₂ = 25. 3 Mpc^-1 for a physical mass of m₂₂ = 8. This outstanding +97. 6% shift maps analytically to an effective non-interacting boson mass of m₂₂, ₄₅₅ 37. 0, placing the framework in full compliance with conservative intergalactic transmission limits without any parameter fine-tuning. We demonstrate why historical free-field bounds (e. g. , Rogers & Peiris 2021) are systematically inapplicable to this architecture due to modified velocity field dynamics. Finally, we formulate an explicit, quantitative prediction for the 1D flux power spectrum down to k 25–50 Mpc^-1 to be tested by upcoming high-resolution data from the Dark Energy Spectroscopic Instrument (DESI).
Irvin Alexis Guerrero Diaz (Tue,) studied this question.