Observational Consequences of Entropy-Geometric Branch Weighting: Boltzmann Brain Suppression, Inflationary Predictions, and the Curved-Space C=1 Extension

Abstract

Paper 1 of this series derived an entropy-weighted branch measure from the C=1 path-integral formulation. In the present work we investigate phenomenological consequences without introducing additional postulates. We analyse the Boltzmann Brain problem, obtaining a characteristic entropy cost ΔS_BB/k_B≈2.66×10⁶⁷ at the present CMB temperature, yielding p_BB/p_OO ≲ exp(−2×10⁶⁷). The framework is extended to curved spacetime, deriving inflationary phenomenology with leading-order predictions ΔP/P=4Ξ_inf, f_NL=0, g_NL=18Ξ_inf for the preferred coupling β=−3/2 — a vanishing bispectrum and nonzero trispectrum constitute a distinctive signature. All predicted deviations remain well below current observational sensitivity. v2 correction (Aug 2026): Paper 1's soliton benchmark (ΔS=−5.39 k_B), mentioned here only as background context from Paper 1, has since been found to correspond to a saddle-point configuration rather than a stable soliton and is now illustrative only (see Paper 1's Correction Note v4). This does not affect any quantitative result in this paper: the Boltzmann Brain suppression bounds are derived independently from the Helmholtz free-energy cost and CMB temperature, and the inflationary predictions depend on the separate coupling β=−3/2, unrelated to the soliton benchmark. The one mention of the withdrawn value has been updated accordingly.