Curvature Variance Exhaustion and the DESI DR2 Observations

In a companion paper (Paper I), we showed that two axioms (curvature conservation and the
holographic entropy bound) produce an effective cosmological constant from a bare Einstein–de
Sitter cosmology. Here we develop the sub-leading correction: curvature variance exhaustion
(CVE), the self-consistent feedback between the emergent geometric correction and structure
formation. CVE produces an apparent evolving equation of state consistent with DESI DR2
within the 2σ contour of the w0–wa plane, without introducing dynamical dark energy. The
framework’s leading-order prediction remains a cosmological constant; the DESI DR2 preference
for w0 > −1, wa < 0 emerges as the transient of the universe’s approach to this constant. We
confront the framework directly with DESI DR2 BAO data, finding ∆χ2 = −3.89 relative to
ΛCDM (BAO alone) and ∆χ2 = −7.21 on combined DESI+Pantheon+ data, with best-fit
Reff = 1.51 h−1 Mpc. Remarkably, fixing Ωm = 1/3 exactly (the DOF counting prediction,
leaving only rd · h as a free parameter) still beats ΛCDM by ∆χ2 = −5.46 with fewer free
parameters—the penalty for fixing Ωm = 1/3 is only ∆χ2 = 1.75 (1.3σ). The CVE dressing
correction reduces the apparent ∼5σ tension between the 2/9 conjecture and data to 1.3σ—
entirely a model-misspecification artifact. We present a suite of additional predictions testable
with DESI, Euclid, eROSITA, SKA, and CMB-S4, including a loosened neutrino mass bound
(Σmν < 0.127–0.137 eV, resolving the emerging tension between DESI DR2’s ΛCDM bound
of 0.064 eV and the oscillation minimum of 0.058 eV), scale-dependent non-Gaussianity from
entropy saturation, and a novel cluster connectivity test where what ΛCDM treats as systematic
lensing contamination, HCV reinterprets as the predicted curvature signal.