What question did this study set out to answer?

The aim is to derive energy density fractions for dark matter, baryonic matter, and dark energy from GF(3) lattice structures.

March 7, 2026Open Access

The Cosmic Budget Solved: ΩDM + Ωb + ΩΛ ≈ 1 from the GF(3) Lattice

Key Points

The aim is to derive energy density fractions for dark matter, baryonic matter, and dark energy from GF(3) lattice structures.
Derived fractions from GF(3) lattice with algebraic calculations
Utilized projective space cardinalities to determine denominators
Compared results to Planck mission values for validation
Calculated dark matter fraction ΩDM = 24/91 (0.2637) with a 1.9% match to Planck
Determined baryonic matter fraction Ωb = 22/455 (0.04835) with a 0.5% match to Planck
Found dark energy fraction ΩΛ = 9/13 (0.6923) with a 0.5% match to Planck
Identified a residual of 0.0044, 48 times larger than observed radiation density, suggesting further investigations.

Abstract

We derive the three energy density fractions of the universe from the GF(3) lattice: dark matter ΩDM = 24/91, baryonic matter Ωb = 22/455, and dark energy ΩΛ = 9/13. The denominators arise from projective space cardinalities: 91 = |P2(GF(9))|, 455 = 5 × 91,13 = |P2(F3)|. The three-component sum is 24/91 + 22/455 + 9/13 = 457/455 = 1.0044, a 0.44% residual above unity. Individual matches: ΩDM = 0.2637 (Planck: 0.2589, 1.9%), Ωb = 0.04835 (Planck: 0.0486, 0.5%), ΩΛ = 0.6923 (Planck: 0.6889, 0.5%). The residual 2/455 ≈ 0.0044 is roughly 48× larger than the observed radiation density Ωr ≈ 10−4; we discuss this discrepancy honestly in Section 4. Despite the imperfect closure, the fact that three independently derived algebraic fractions land within 1–2% of Planck values is a strong structural constraint.

The Cosmic Budget Solved: ΩDM + Ωb + ΩΛ ≈ 1 from the GF(3) Lattice

Key Points

Abstract

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