The Cosmic Isolation Scale: Quarks in de Sitter Space

When Local Binding Meets Global Expansion

The Fundamental Paradox

While gluons continue to bind quarks into hadrons due to the immense strength of the strong nuclear force, the exponential expansion of de Sitter space creates distances so vast that atomic nuclei cannot form. The scale of separation between bound quark systems becomes astronomical compared to nuclear scales.

Nuclear Binding Scale

~1 femtometer (10⁻¹⁵ m)

The characteristic distance for quarks within a proton or neutron, and for nucleons within an atomic nucleus. The strong nuclear force operates effectively at this scale.

de Sitter Isolation Scale

~10⁴¹ meters

The characteristic separation between remaining bound quark systems in the late de Sitter epoch. This is 56 orders of magnitude larger than nuclear scales.

Scale Ratio: 10⁵⁶ to 1

The de Sitter Horizon Scale

The fundamental length scale in de Sitter space is set by the cosmological horizon. For our universe's current dark energy density, this is approximately:

~10²⁶ meters (Current Hubble Scale)

However, as the universe continues to expand and matter dilutes, the effective separation between any remaining bound quark systems grows exponentially. In the asymptotic de Sitter state, the typical distance between such systems approaches scales where the expansion rate prevents any causal contact.

Why Nuclei Cannot Form

For an atomic nucleus to form, protons and neutrons must come within 1-10 femtometers of each other. Several cosmic factors prevent this:

Dilution Effect: The number density of particles drops as the universe volume increases. In late de Sitter phase, the average separation between any two particles grows exponentially.

Horizon Limitation: The cosmological horizon represents the maximum distance for causal contact. Particles beyond this distance can never interact.

Expansion Dominance: The expansion rate between two test particles exceeds the relative velocity they could achieve through any physical force.

Electromagnetic Screening: Even if protons could approach, their positive charges would repel at distances much larger than nuclear scales.

The Hierarchy of Binding Forces

Different fundamental forces become ineffective at different cosmic scales:

Strong Nuclear Force: Effective to ~10⁻¹⁵ m. Always binds quarks locally but cannot act over cosmic distances.

Electromagnetic Force: Effective to astronomical scales but screened by charge separation in late universe.

Gravitational Force: The only force with infinite range, but far too weak to overcome cosmic expansion at particle scales.

Cosmic Conclusion

In the de Sitter epoch, quarks remain bound into individual hadrons by the strong nuclear force operating at femtometer scales, but the cosmic separation between these bound systems grows to approximately 10⁴¹ meters—a scale so vast that the formation of atomic nuclei becomes mathematically impossible.

The universe contains bound quark systems forever isolated from one another by distances that make our current observable universe seem microscopic in comparison. Local quantum binding persists while global structure formation becomes eternally impossible.

Isolation Complete: ~10¹⁰⁰ years