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.