Renormalization group of the gravity coupled with the scalar theory and its effective normalization

TL;DR

This paper investigates the renormalization group flow of gravity coupled with scalar fields, focusing on the normalization of the quantum-corrected action across different energy scales to address divergence issues.

Contribution

It introduces a normalization approach for Einstein-Hilbert and scalar-coupled gravitational actions that accounts for cutoff dependence from infrared to ultraviolet scales.

Findings

Renormalization group flow clarifies cutoff dependence in quantum gravity.

Normalization improves the consistency of quantum-corrected gravitational actions.

The approach bridges classical and quantum gravity regimes.

Abstract

The normalization of the quantum corrected action is resolving the equation divergent dependence of the cutoff towards the system apparent result in quantum gravity. Here we consider the normalization to Einstein R twice scalar action with the cutoff runs from apparent infrared momentu to the ultraviolet momentum. These gravitational actions, Einstein R twice and Einstein R twice with the scalar theory, are come to the ensured apparent system recommendations in classical quantum gravity.