On the Cutoff Scale Identification of FLRW Cosmology in Asymptotically Safe Gravity

TL;DR

This work applies FRG-improved Einstein equations within asymptotically safe gravity to late-time FLRW cosmology, focusing on running couplings $G(k)$ and $\\Lambda(k)$ from the Einstein–Hilbert truncation and the identification of the infrared cutoff $k$ with cosmological scales. It distinguishes two RG trajectory branches, $\\Lambda_0=0$ (Type IIa) and $\\Lambda_0\neq0$ (Type IIIa), and shows that viable cutoff identifications differ by branch: for $\\Lambda_0=0$ identifying $k$ with the classical Hubble parameter $H_{\rm cl}$ yields a quantum-corrected evolution with a finite critical time $t_c$ separating AdS- and dS-like phases, while for $\\Lambda_0>0$ identifying $k$ with a function of the scale factor via $k=\\xi/\\tau$ (with $\\tau\propto a_{\rm cl}^{2\alpha}$) produces a consistent late-time cosmology under a modified continuity equation. The case $k=\\xi/t$ fails for $\\Lambda_0>0$, highlighting the sensitivity of quantum-corrected cosmology to cutoff choices. Overall, the paper demonstrates how FRG running introduces a new physical scale and breaks time-translation symmetry, providing guidance on physically viable cutoff identifications in quantum-corrected cosmology.

Abstract

We examine Friedmann-Lemaître-Robertson-Walker cosmology, incorporating quantum gravitational corrections through the functional renormalization group flow of the effective action for gravity. We solve the Einstein equation with quantum improved coupling perturbatively including the case with non-vanishing classical cosmological constant (CC) which was overlooked in the literatures. We discuss what is the suitable identification of the momentum cutoff $k$ with time scale, and find that the choice of the Hubble parameter is suitable for vanishing CC but not so for non-vanishing CC. We suggest suitable identification in this case. The energy-scale dependent running coupling breaks the time translation symmetry and then introduces a new physical scale.