Finiteness of piecewise flat quantum gravity with matter

TL;DR

This paper reviews a piecewise flat quantum gravity approach with matter, demonstrating the finiteness of the path integral under specific conditions and discussing its implications for cosmology and the universe's wavefunction.

Contribution

It introduces a finite path integral formulation of quantum gravity coupled with matter using triangulated manifolds, with conditions on edge lengths.

Findings

Path integral is finite for negative power > 52.5 of edge lengths squared.

The approach relates the effective action to the universe's wavefunction.

It suggests a natural emergence of Starobinsky inflation.

Abstract

We review the approach to quantum gravity which is based on the assumption that the short-distance structure of the spacetime is given by a piecewise flat manifold corresponding to a triangulation of a smooth manifold. We then describe the coupling of the Standard Model to this quantum gravity theory and show that the corresponding path integral is finite when the negative power of the product of the edge lengths squared in the path-integral measure is chossen to be grater than 52,5. The implications of this result are discussed, which include a relationship between the effective action and a wavefunction of the universe, the existence of the non-perturbative effective action, the correct value of the cosmological constant and the natural appearence of the Starobinsky inflation.