🌀 UNNS.Tech Research Brief: A Recursive Framework for the Hubble Tension
By the UNNS Research Collective (2025-10) — UNNS Lab v0.4.0
Abstract
The so-called Hubble tension — the persistent ≈ 8–10 % discrepancy between local (Cepheid / SNe) and early-universe (CMB / Planck) determinations of the Hubble constant H₀ — is re-interpreted here from a Unbounded Nested Number Sequences (UNNS) perspective. What appears as a cosmological inconsistency is understood instead as the natural outcome of dual attractor states within the recursive curvature dynamics of the τ-field substrate. We show how recursion-depth stratification, τ-phase variance, and entropy-driven curvature bifurcations can yield distinct effective expansion rates at different observational regimes. Implications for observational cosmology, entropy–expansion susceptibility, and predictive tests are outlined.
1 · Introduction
The Hubble constant remains among the most contested quantities in modern cosmology.
Early-universe probes yield
H₀ ≈ 67.4 km s⁻¹ Mpc⁻¹,
whereas local distance-ladder methods return higher values near
73 km s⁻¹ Mpc⁻¹.
Standard explanations invoke new physics, unaccounted biases, or unmodelled complexities.
In contrast, the UNNS framework suggests that this divergence is not a flaw
but an inherent property of recursion:
observers measure different recursion-depth eigenvalues of the same τ-field substrate.
2 · UNNS Recursion and Cosmological Expansion
2.1 Recursive Curvature Dynamics
Φₙ₊₁ = Φₙ + βₙ ∇²Φₙ κₙ = ∇²Φₙ + βₙ |∇Φₙ|²
Each iteration index n labels recursion depth, not chronological time. The τ-variable encodes recursive phase:
τₙ = e^{2πi qₙ / Q₀ + δθ}
where δθ is a Gaussian perturbation with noise amplitude σ.
2.2 Emergent Expansion Eigenvalue
The apparent cosmic expansion arises as mean curvature drift across recursion layers:
H₀(n) = (1 / Δtₙ) ⟨ ΔΦₙ / Φₙ ⟩
Thus H₀ becomes a layer-specific eigenvalue rather than a single universal constant.
3 · Bifurcation Hypothesis and the Hubble Tension
3.1 Dual-Attractor Interpretation
- Low-entropy attractor → deep-layer recursion (CMB regime) → lower H₀
- High-entropy attractor → near-surface recursion (local universe) → higher H₀
The effective parameterisation:
H₀(σ_τ) = H_∞ [ 1 + ξ ( σ_τ² / σ_c² − σ_τ² ) ]
where ξ is a coupling constant and σ_c the critical τ-noise. Even modest σ_τ fluctuations (~10 %) reproduce observed H₀ shifts.
3.2 Observational Mapping
- CMB/Planck → deep recursion (low σ_τ) → ≈ 67 km s⁻¹ Mpc⁻¹
- Local SNe/Cepheid → higher-noise domains → ≈ 73 km s⁻¹ Mpc⁻¹
Entropy accumulated during structure formation increases σ_τ locally, shifting the effective recursion eigenvalue.
4 · Predictive Framework and Tests
4.1 Entropy–Expansion Susceptibility
χ_τ = ∂H₀ / ∂H_r
where H_r is the recursive-entropy metric of the τ-field. A positive χ_τ would empirically support the UNNS interpretation.
4.2 Further Predictions
- Gradual running of H(z) with redshift as τ-variance grows.
- Correlation between large-scale entropy proxies (e.g., matter clustering) and local H₀ measurements.
- Intermediate attractor states in structure-rich regions showing slight local expansion differences.
5 · Implications for Cosmology
5.1 Re-conceptualising Constants
Within UNNS, H₀ is not immutable but a recursion-attractor value. The Hubble tension marks coexistence of multiple curvature-substrate attractors.
5.2 Unified Recursion Physics
This interpretation bridges small-scale τ-Field Chamber phenomena with cosmological expansion: both arise from recursive dynamics subject to entropy-phase bifurcation.
5.3 Methodological Shift
Cosmology must transition from parameter fitting to recursion-layer diagnostics. Observations should be contextualised by recursion depth, τ-phase variance, and entropy generation rather than assuming a single global expansion rate.
6 · Conclusion
The Hubble tension becomes not a crisis but a signal of recursive stratification. Observers at different τ-depths perceive distinct expansion eigenvalues.
“Constants emerge as attractors of recursion. What appears as tension is the signature of a layered substrate.”
The framework calls for empirical tests: measure χ_τ, correlate H₀ with entropy proxies, and search for intermediate attractors. Cosmic expansion thus becomes a multi-layer eigenstructure of recursive curvature — a living record of how the universe organises its own unfolding.
UNNS Research Collective (2025)
UNNS Lab v0.4.0 · Cosmological Applications of Recursive Curvature Dynamics