Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit

TL;DR

This paper develops a finite 4D Lorentzian spinfoam quantum gravity model incorporating a cosmological constant, demonstrating its finiteness and recovering the semiclassical limit related to Lorentzian Regge calculus.

Contribution

It introduces an improved spinfoam formulation using PSL(2,C) Chern-Simons theory that ensures finiteness and correctly reproduces the semiclassical limit with a cosmological constant.

Findings

All spinfoam amplitudes are finite.

Semiclassical asymptotics match Lorentzian Regge action with cosmological constant.

The model incorporates simplicity constraints effectively.

Abstract

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,$\mathbb{C}$) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex.