GRAV In the literature: contested

Do spin foam models reproduce curved solutions of Einstein's equations?

In plain words

Loop quantum gravity's sum over spacetime histories, called a spin foam, should reduce to Einstein's theory for large geometries. Calculations suggest that the standard model of this sum favors flat geometries, which would leave out the curvature that is gravity.

Precise statement

For the EPRL-FK spin foam amplitude on a fixed 4D triangulation, the large-spin limit of each vertex amplitude gives the Regge action (the discrete Einstein-Hilbert action on a triangulation), but the spin sum appears dominated by configurations with vanishing deficit angles, the flatness problem (Hellmann and Kaminski 2013). Determine whether, under refinement or coarse-graining at fixed Barbero-Immirzi parameter $\gamma$, the amplitude is dominated by discrete geometries approximating curved solutions of Einstein's equations. An answer is an asymptotic or numerical demonstration in a refinement limit, or a proof of dominance by flat configurations.

What would settle it

An asymptotic or numerical evaluation of the EPRL amplitude under refinement showing whether curved Regge solutions dominate.

Status in the literature

Unverified note

Modified effective spin foam models recover curved dynamics (Asante, Dittrich, Haggard 2020); the behavior of the EPRL amplitude is disputed as of 2026.