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

TL;DR

This paper investigates quantum gravitational effects on FLRW cosmology using the functional renormalization group, addressing cutoff scale identification issues especially with non-zero cosmological constant.

Contribution

It introduces a novel approach to identify the cutoff scale in quantum-corrected FLRW cosmology, including cases with non-zero classical cosmological constant.

Findings

Hubble parameter is suitable for cutoff identification when CC is zero

Proposes a new cutoff identification method for non-zero CC cases

Quantum corrections break time translation symmetry, introducing a new physical scale

Abstract

We examine Friedmann-Lema\^itre-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.