Major Conjectures and Cosmological Tests P: The Cosmological Falsifiability of the Conformal Bootstrap

This paper proposes a cosmological test framework based on the axioms of information conservation and computability, applying the conformal bootstrap methodfrom quantum field theory to the analysis of primordial perturbations in the earlyinflationary universe. By assuming approximate conformal invariance during inflation, we derive that the convergence of the operator product expansion for theprimordial perturbation field imposes a unique constraint on the amplitude decaylaw of the cosmic microwave background (CMB) temperature fluctuation threepoint function in the folded configuration region. Under the axioms of informationconservation and computability, the lower bound on the operator dimension, ∆min,is mapped to the exponential decay index β = 2∆min−3 of the three-point functionin the folded limit. The theoretical prediction yields a decay index of β = 2.18±0.09.Measurements using Planck 2018 data yield βobs = 2.22 ± 0.11, showing high consistency with the prediction. Future experiments such as CMB-S4 are expected totest this prediction with higher precision, thereby providing a clear falsifiable pathfor the applicability of the conformal bootstrap in cosmology.