Fossil Gravity: A Parameter-Free Derivation of the Dark Energy Equation of State from the ZS Term via LIGO GWTC-3

Abstract: DESI DR2 (March 2025, 4. 2σ) finds w₀ = −0. 752 ± 0. 059, ruling out a cosmological constant. Wepresent the first parameter-free derivation of the dark energy equation of state w (z) within fossil gravitytheory (Wartenberg 2026). The theory's Zₛ term describes spacetime curvature produced by causalcondensation in Zone 0 — without a mass source term. From Supplement VII, Eq. VII-29, the scalingGBHμν ∝ M² implies a cosmological energy density ρZS (z) = (4πG/ℏc³) ·⟨M²⟩·nBH, where ⟨M²⟩ isthe mean squared total mass and nBH the comoving number density of stellar-mass black holes. Bothquantities are computable directly from gravitational wave catalogs — without any fit to cosmologicaldata. The effective equation of state wZS (z) = −1 + (1/3) ·dlnρZS/dlna deviates structurally from −1without free parameters; this prediction follows from the M² scaling alone. Using GWTC-3 (81 BBHevents, z = 0. 05–0. 83), we compute ρZS (z) and derive wZS (z) directly from observations. Currentresults are limited by LIGO selection effects. Selection-corrected results with LIGO O4 data (∼200events) are identified as the critical quantitative test. Falsifiable prediction: if wZS (0) falls outside theDESI band, the Zₛ interpretation of dark energy is ruled out. Keywords: fossil gravity · dark energy · equation of state · Zₛ term · causal condensation · LIGO GWTC-3 · DESIDR2 · black hole population · w (z)