Wayne Lundberg · Theoretical Cosmology · QCD Portal
jR
Settling the Cosmological Coincidence Problem via a dynamic scalar coupling between SU(3) flux-tube geometry and the universal expansion factor R(t).
The Coincidence Problem
In the standard ΛCDM cosmological model, matter density (ρm) dilutes as
(1+z)³ as the universe expands, while Dark Energy density (ρΛ) remains
perfectly constant — a cosmological constant. This means at almost every epoch in cosmic history,
one of them vastly dominates the other.
Yet we observe today that ρΛ ≈ 2.3 × ρm — they are within an order of magnitude of each other, something that only happens during an incredibly brief window of cosmic time. Why does life evolve precisely in this epoch? This is the Coincidence Problem.
Yet we observe today that ρΛ ≈ 2.3 × ρm — they are within an order of magnitude of each other, something that only happens during an incredibly brief window of cosmic time. Why does life evolve precisely in this epoch? This is the Coincidence Problem.
Key Question: Is this a cosmic accident requiring fine-tuning of initial conditions
to 1 part in 10¹²², or does some physical mechanism enforce the near-equality?
The jR Hypothesis
The jR hypothesis proposes that the vacuum energy is not a constant,
but is dynamically coupled to the SU(3) chromodynamic flux manifold of the Strong Force.
The key insight: when we treat the quantum vacuum as a dynamic topological lattice — the same lattice structure that confines quarks via flux tubes — we find that vacuum energy naturally "tracks" matter density as the universe expands.
The scalar parameter j mediates the coupling between the gluon condensate and the Hubble expansion rate H(t), while R(t) is the cosmic scale factor. Together, jR defines a dimensionless ratio that stabilises near unity.
The key insight: when we treat the quantum vacuum as a dynamic topological lattice — the same lattice structure that confines quarks via flux tubes — we find that vacuum energy naturally "tracks" matter density as the universe expands.
The scalar parameter j mediates the coupling between the gluon condensate and the Hubble expansion rate H(t), while R(t) is the cosmic scale factor. Together, jR defines a dimensionless ratio that stabilises near unity.
Mechanism: As matter density decreases during expansion, the gluon condensate
(related to ΛQCD) responds via the jR coupling — reducing vacuum energy proportionally.
This is not fine-tuning; it is a consequence of QCD's topology.
Cosmic Density Evolution
Blue: Matter density ρm(z) ∝ (1+z)³ — dilutes as universe expands.
Purple: Standard Λ (constant) dark energy.
Gold: jR-coupled vacuum energy — tracks matter density.
The jR field eliminates the fine-tuning of the crossing point.
Connection to QCD & Proton Stability
The jR framework has direct implications for the proton lifetime problem.
If vacuum energy couples to the gluon condensate, then baryon number violation processes
(p → e⁺ + π⁰) mediated by GUT-scale leptoquarks are also modulated by the jR field.
A dynamical vacuum means the effective GUT scale MX may have evolved over cosmic time, which shifts the predicted proton lifetime — and may explain why no decay has been observed despite decades of Super-Kamiokande data.
A dynamical vacuum means the effective GUT scale MX may have evolved over cosmic time, which shifts the predicted proton lifetime — and may explain why no decay has been observed despite decades of Super-Kamiokande data.
Research Target: τ(p→e⁺π⁰) > 1.6×10³⁴ yr (Super-K lower bound).
The jR correction to MX could raise the prediction above experimental reach —
or predict a revised channel hierarchy.
Key Physical Insights
- QCD/Cosmo Duality The same string tension σ ≈ 0.18 GeV² that confines quarks appears in the jR coupling to cosmological expansion. Confinement and dark energy share a topological origin.
- Dynamic Vacuum The vacuum is not an inert background — it is a fluctuating SU(3) gauge field condensate whose energy responds to the matter content of the universe.
- No Fine-Tuning The near-equality ρΛ ≈ ρm today emerges naturally from the jR attractor solution — the field equation has a stable fixed point at jR ≈ 1.
- Testable Predictions jR predicts a small equation-of-state deviation w(z) ≠ −1, detectable with next-generation CMB and BAO surveys (DESI, Euclid, CMB-S4).