Quantum Gravity from dynamical metric fluctuations

TL;DR

This paper explores the asymptotic safety scenario in quantum gravity by analyzing dynamical metric fluctuations using a functional renormalisation group approach, addressing both Euclidean and Lorentzian signatures and their implications.

Contribution

It introduces a detailed derivation of flow equations for dynamical metric fluctuations and reviews recent results on correlation functions, phase structure, and spectral properties in asymptotically safe gravity.

Findings

Correlation functions at vanishing cutoff scale analyzed

Phase structure of asymptotically safe Standard Model reviewed

Spectral properties of gravity in Lorentzian space-times computed

Abstract

In this contribution, we discuss the asymptotic safety scenario for quantum gravity by evaluating the correlation functions of dynamical metric fluctuations. This is done with a functional renormalisation group approach that disentangles dynamical metric fluctuations from the background metric. We detail the derivation of the respective flow equations on space-time manifolds with Euclidean and Lorentzian signatures and discuss the diffeomorphism symmetry constraints on the flow as well as the convergence of systematic vertex expansion schemes. We then proceed with a comprehensive review of results of momentum-dependent correlation functions at vanishing cutoff scale, the phase structure of the asymptotically safe Standard Model, and spectral properties of asymptotically safe gravity from direct computations in space-times with Lorentzian signatures such as the graviton spectral function.