Asymptotic safety and the cosmological constant

TL;DR

This paper investigates the non-perturbative renormalisation of quantum gravity, revealing an asymptotically safe fixed point that could explain the smallness of the cosmological constant and align with lattice results.

Contribution

It demonstrates the existence of an asymptotically safe fixed point in quantum gravity that predicts a vanishing cosmological constant and matches lattice critical exponents.

Findings

Existence of an asymptotically safe fixed point in quantum gravity.

Fixed point predicts a zero cosmological constant across scales.

Reproduces lattice critical exponent $ u=1/3$, indicating physical relevance.

Abstract

We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. If only the conformal fluctuations are quantised we find an asymptotically safe fixed point predicting a vanishing cosmological constant on all scales. At this fixed point we reproduce the critical exponent, $\nu = 1/3$, found in numerical lattice studies by Hamber. This suggests the fixed point may be physical while solving the cosmological constant problem.