What question did this study set out to answer?

To derive an analytical expression for dark energy density fraction and explore its geometric implications.

April 17, 2026Open Access

An Analytical Expression for the Dark Energy Density Fraction from Holographic UV/IR Coupling

Key Points

To derive an analytical expression for dark energy density fraction and explore its geometric implications.
Derived constants C₀ and Ω_Λ from first principles.
Established the geometric interpretation of C₀.
Extended framework to study comprehensive geometric constraints covering vast scales.
Calculated C₀ and Ω_Λ yields approximately 0.6994.
Provided two precise verifications at 0.06% and 0.00% accuracy.
Developed a universal dynamical equation connecting Casimir physics to dark energy.

Abstract

A three-paper series on holographic dark energy. Paper I derives C₀ = π²/ (16e²) and Ω_Λ = π³/ (6e²) ≈ 0. 6994 from first principles, independent of the Hubble tension. Paper II establishes the geometric interpretation and scope of C₀. Paper III extends the framework to a unified geometric constraint C (R, τ) spanning 61 orders of magnitude, with two precise verifications (0. 06% and 0. 00%) and a universal dynamical equation linking Casimir physics to dark energy.

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