On Spinfoams Near a Classical Curvature Singularity

TL;DR

This paper uses spinfoam models within covariant Loop Quantum Gravity to analyze the behavior of space-time near classical curvature singularities, revealing quantum effects, phase transitions, and long-range correlations.

Contribution

It demonstrates that near singularities, spinfoam configurations involve small spins indicating strong quantum effects and proposes a phase transition framework in covariant LQG.

Findings

Near singularities, spinfoams involve small spins with significant quantum effects.

A phase transition occurs between low and high curvature regions in covariant LQG.

Long-range spin correlations are present in the low curvature phase.

Abstract

We apply the technique of spinfoam to study the space-time which, classically, contains a curvature singularity. We derive from the full covariant Loop Quantum Gravity (LQG) that the region near curvature singularity has to be of strong quantum gravity effect. We show that the spinfoam configuration describing the near-singularity region has to be of small spins $j$, in order that its contribution to the full spinfoam amplitude is nontrivial. The spinfoams in low and high curvature regions of the space-time may be viewed as in two different {phases} of covariant LQG. There should be a phase transition as the space-time described by spinfoam becomes more and more curved. A candidate of order parameter is proposed for understanding the phase transition. Moreover, we also analyze the spin-spin correlation function of spinfoam, and show the correlation is of long-range in the low curvature phase. This work is a first step toward understanding the physics of black hole and early universe from the full covariant LQG theory.