Searching for classical geometries in spin foam amplitudes: a numerical method

Abstract

We develop a numerical method to investigate the semiclassical limit of spin foam amplitudes with many vertices. We test it using the Ponzano-Regge model, a spin foam model for three-dimensional euclidean gravity, and a transition amplitude with three vertices. We study the summation over bulk spins, and we identify the stationary phase points that dominate it and that correspond to classical geometries. We complement with the numerical analysis of a four vertex transition amplitude and with a modification of the model that includes local curvature. We discuss the generalization of our results to the four-dimensional EPRL spin foam model, and we provide suggestions for new computations.

Primordial Fluctuations From Quantum Gravity

“…We found that the cosmological state is highly non-typical, showing an entanglement entropy that is apparently reaching an asymptotic value as the scale factor increases. Our work is one of the first explorations of the purely quantum regime of LQG-without resorting to the highspin semiclassical limit of the theory-and one of the first applications to a concrete physical model of the numerical tools that are recently being developed for covariant Loop Quantum Gravity (Bianchi et al, 2018;Donà et al, 2019;Dona et al, 2020). Our results indicate that an early quantum phase of the universe may provide an explanation for known puzzling features of the standard cosmological model, such as the horizon problem, possibly even without introducing additional inflationary and/or bouncing phases.…”

Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude

“…Another possibility is to implement the recursion relations for the SL(2, C) Clebsch-Gordan coefficients derived in [48]. For a simpler model with three-valent boosters and no intertwiners, this approach is extremely powerful, and one can push the internal sums to order ∆ ∼ 100 [49].…”

Renormalization of Group Field Theories for Quantum Gravity: New Computations and Some Suggestions

“…These new results should be added to other ones we have on the calculation of radiative corrections and basic divergences of both Riemannian and Lorentzian simplicial spin foam models, and on explicit evaluations of their building blocks (mainly the vertex amplitudes). For a partial list, see [41][42][43][44][45][46][47][48][49] and references therein. Future progress will build on these hardwon calculations.…”