Quantum gravity on foliated spacetime - asymptotically safe and sound

TL;DR

This paper investigates the asymptotic safety of quantum gravity using a foliated spacetime approach, revealing a second non-Gaussian fixed point that ensures well-defined trajectories and a dynamically vanishing cosmological constant.

Contribution

It introduces a new fixed point in the gravitational renormalization group flow within the ADM formalism, enhancing the understanding of quantum gravity's phase structure.

Findings

Identification of a second non-Gaussian fixed point with positive Newton's constant

All RG trajectories connected to classical GR are well-defined across scales

Dynamical driving of the cosmological constant to zero in the infrared

Abstract

Asymptotic Safety provides a mechanism for constructing a consistent and predictive quantum theory of gravity valid on all length scales. Its key ingredient is a non-Gaussian fixed point of the gravitational renormalization group flow which controls the scaling of couplings and correlation functions at high energy. In this work we use a functional renormalization group equation adapted to the ADM-formalism for evaluating the gravitational renormalization group flow on a cosmological Friedmann-Robertson-Walker background. Besides possessing the UV-non-Gaussian fixed point characteristic for Asymptotic Safety the setting exhibits a second non-Gaussian fixed point with a positive Newton's constant and real critical exponents. The new fixed point alters the phase diagram in such a way that all renormalization group trajectories connected to classical general relativity are well-defined on all length scales. In particular a positive cosmological constant is dynamically driven to zero in the deep infrared. Moreover, the scaling dimensions associated with the universality classes emerging within the causal setting exhibit qualitative agreement with results found within the $\epsilon$-expansion around two dimensions, Monte Carlo simulations based on Lattice Quantum Gravity, and the discretized Wheeler-deWitt equation.