Functional Renormalization Group flows on Friedman-Lema\^{\i}tre-Robertson-Walker backgrounds

TL;DR

This paper revisits the gravitational functional renormalization group equation in the ADM formulation, connecting it to covariant methods and Causal Dynamical Triangulations, with detailed analysis on Einstein-Hilbert projections.

Contribution

It introduces a new connection between the ADM-based FRG formalism and Causal Dynamical Triangulations, expanding the understanding of quantum gravity approaches.

Findings

Detailed review of RG flow on FLRW backgrounds.

Connection established between ADM formalism and CDT.

Insights into Einstein-Hilbert action projections.

Abstract

We reanalyze the construction of the gravitational functional renormalization group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing its connection to the covariant formulation. The results obtained from projecting the renormalization group flow onto the Einstein-Hilbert action are reviewed in detail and we provide a novel example illustrating how the formalism may be connected to the Causal Dynamical Triangulations approach to quantum gravity.