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Jaehong Oh

χPreprint · 2025

Quantum Bounce Singularity Resolution in Loop Quantum Gravity with Internal Time

Jaehong Oh

130 words1 min read

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Abstract

We present a kinematic framework demonstrating how Loop Quantum Gravity (LQG) discreteness naturally avoids the Big Bang singularity. Using an internal time functional T[γ] = ∫⟨∇Φ,γ̇⟩/‖∇Φ‖² dt defined on spin network configuration space, we evaluate quantum observables along a prescribed bounce trajectory in a 2-node toy model. Our results demonstrate: (1) the scale factor reaches a finite minimum a_min = 0.707 ℓ_P > 0, avoiding the classical singularity a → 0; (2) energy density remains bounded ρ_max = 6.849 < ∞ (in Planck units); (3) the Hubble parameter smoothly transitions from H < 0 (contraction) through H = 0 (bounce) to H > 0 (expansion). These findings provide direct numerical confirmation of LQC's central prediction: quantum discreteness of geometry replaces the Big Bang singularity with a smooth bounce at Planck scale.

Overview

A kinematic demonstration that LQG's discrete geometry resolves the Big Bang singularity by replacing it with a smooth bounce at Planck scale. The technical contribution is an internal-time functional — inspired by Fisher information geometry — that lets us evaluate quantum observables directly on spin-network configuration space without invoking an external clock.

What the paper shows

  • Singularity avoidance: a_min = 0.707 ℓ_P, well above the classical zero.
  • Bounded energy density: ρ_max = 6.849 in Planck units.
  • Smooth bounce: the Hubble parameter sweeps H < 0 → H = 0 → H > 0 across the transition.
  • Three properties of the internal-time functional proved: reparametrisation invariance, direction sensitivity, and clock-choice invariance.

Where it sits

The first paper in a three-part sequence on LQG with internal time — companion pieces are internal-time GR emergence and the scalable simulations paper.

BibTeX· generated

@misc{oh2025lqg,
  title   = {Quantum Bounce Singularity Resolution in Loop Quantum Gravity with Internal Time},
  author  = {Jaehong Oh},
  year    = {2025},
  url     = {https://jack0682.github.io/papers/lqg-quantum-bounce/},
}