Spin Network Wavefunction and the Graviton Propagator

TL;DR

This paper demonstrates that the large-spin asymptotics of the flat-spacetime wavefunction in Loop Quantum Gravity leads to the correct graviton propagator behavior at large distances, independent of the spin foam model used.

Contribution

It establishes a nonperturbative link between the wavefunction's asymptotics and the graviton propagator, clarifying the role of the Hamiltonian constraint and the spin parameter in Rovelli's ansatz.

Findings

Graviton propagator has correct large-distance asymptotics

Wavefunction asymptotics are model-independent

Spin parameter in Rovelli's ansatz explained

Abstract

We show that if the flat-spacetime wavefunction in the spin network basis of Loop Quantum Gravity has a large-spin asymptotics given by Rovelli's ansatz then the corresponding graviton propagator has the correct large-distance asymptotics nonperturbatively and independently of the spin foam model used to describe the evolution operator. We also argue that even in the Rovelli approach the wavefunction should satisfy the Hamiltonian constraint and we give an explanation for the spin parameter appearing in Rovelli's ansatz.