Planck Scale Cosmology and Asymptotic Safety in Resummed Quantum Gravity

TL;DR

This paper demonstrates how resummed quantum gravity can reproduce asymptotic safety behavior, providing first principles predictions for fundamental constants and supporting Planck scale cosmology.

Contribution

It extends Feynman's formulation to recover UV fixed-point behavior, aligning with Wilsonian and Dyson-Schwinger renormalization results, and offers first principles predictions for gravitational constants.

Findings

Reproduces asymptotic safety fixed point from resummed series

Predicts dimensionless gravitational and cosmological constants

Supports Planck scale cosmology model

Abstract

In Weinberg's asymptotic safety approach, a finite dimensional critical surface for a UV stable fixed point generates a theory of quantum gravity with a finite number of physical parameters. We argue that, in an extension of Feynman's original formulation of the theory, we recover this fixed-point UV behavior from an exact re-arrangement of the respective perturbative series. Our results are consistent with the exact field space Wilsonian renormalization group results of Reuter {\it et al.} and with recent Hopf- algebraic Dyson-Schwinger renormalization theory results of Kreimer. We obtain the first "first principles" predictions of the dimensionless gravitational and cosmological constants and our results support the Planck scale cosmology of Bonanno and Reuter. We conclude with an estimate for the currently observed value of the cosmological constant.