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Curvature Variance Exhaustion and the DESI DR2 Observations

Authors: Culm Macaday, Sean Eric;

Curvature Variance Exhaustion and the DESI DR2 Observations

Abstract

In a companion paper (Paper I), we showed that two axioms (curvature conservation and theholographic entropy bound) produce an effective cosmological constant from a bare Einstein–deSitter cosmology. Here we develop the sub-leading correction: curvature variance exhaustion(CVE), the self-consistent feedback between the emergent geometric correction and structureformation. CVE produces an apparent evolving equation of state consistent with DESI DR2within the 2σ contour of the w0–wa plane, without introducing dynamical dark energy. Theframework’s leading-order prediction remains a cosmological constant; the DESI DR2 preferencefor w0 > −1, wa < 0 emerges as the transient of the universe’s approach to this constant. Weconfront the framework directly with DESI DR2 BAO data, finding ∆χ2 = −3.89 relative toΛCDM (BAO alone) and ∆χ2 = −7.21 on combined DESI+Pantheon+ data, with best-fitReff = 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 freeparameters—the penalty for fixing Ωm = 1/3 is only ∆χ2 = 1.75 (1.3σ). The CVE dressingcorrection 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 testablewith 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 boundof 0.064 eV and the oscillation minimum of 0.058 eV), scale-dependent non-Gaussianity fromentropy saturation, and a novel cluster connectivity test where what ΛCDM treats as systematiclensing contamination, HCV reinterprets as the predicted curvature signal.

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