Theoretical work models cosmological history within a single axiom, suggesting insights into dark matter and dark energy.
This work treats cosmological history within a unified framework built upon a single minimal axiom — the background space is three-dimensional (D = 3) — and structural assumptions that either derive from this axiom or are read as preconditions of its physical consistency. In the framework, n is the spatial dimensional density of the form residing in D = 3 space and takes values in the open interval n ∈ (0, 4). Four active regimes — Planck-floor (d = 0), string (d = 1), surface/energy (d = 2), volumetric matter (d = 3) — are organized by the form-energy ledger E_n = x^n; the Z₂ symmetry n ↔ 4 − n is centered at n = 2. The extreme values n = 0 and n = 4 are physically inaccessible; these are not a separate assumption but the kinematic consequence of the single axiom. The dynamical mechanism is a cyclic dimensional flow: in the surface regime area accumulation exceeds the n = 3 threshold; in the volumetric matter regime, since no new upper dimension can open, energy-matter conversion is forced into single-channel matter accumulation and gravitational backreaction internally produces black holes. The descent continues down to the n → 0⁺ Planck-floor, where bouncing takes over. With the canonical potential V(φ) = Λ⁴ cosh[β(φ − φ★)/M] and the modified Friedmann equation H² = (ρ/3M²)[1 − ρ/ρ_b], ρ_b = 2M⁴/cosh(u), the structure supports double-bouncing. Dark energy is the late-time manifestation of the transformation energy released at form-transitions (ΣQ = x⁴ − 1); dark matter is not a separate entity but the gravitational appearance of local n deviation (Δn). The cycle-residue principle accounts for mature structures in the early universe. The central prediction w(z) = −1 + ε₀(1 + z)^(2β_eff²) is testable with DESI DR2, Euclid and LSST; the structural w ≥ −1 bound of the framework is consistent with the late-time (z ≲ 0.5) quintessence-like behavior indicated by DESI DR2, while the high-redshift phantom-crossing signal is discussed as a parametrization-dependent appearance (Section 13.1).
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Hamdi Barut (2026) studied this question.
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