Thermal RG flow of AS quantum gravity. Physics Letter B, 864 (2025) 139440

Abstract

We perform the thermal Renormalization Group (RG) study of the Asymptotically Safe (AS) quantum gravity in the Einstein-Hilbert truncation by relating the temperature parameter to the running RG scale as 𝑇 ≡ 𝑘𝑇 = 𝜏𝑘(in natural units) in order to determine its thermal evolution in terms of the dimensionless temperature 𝜏 which is associated with the temperature of the expanding Universe. Thus, 𝑘𝑇 and 𝑘 are understood as running cutoffs for thermal and quantum fluctuations, respectively. Quantum effects are taken into account by moving along the thermal RG trajectory with fixed value of 𝜏 producing the quantum effective action at a given dimensionless temperature. The 𝜏-evolution of the dimensionless Newton coupling 𝑔(𝜏) and the dimensionless cosmological constant 𝜆(𝜏) results in a vanishing 𝑔-coordinate of the Reuter (i.e., non-Gaussian UV) fixed point in the high temperature limit (𝜏 → ∞) which means that only the symmetric phase of AS gravity survives at 𝜏 =∞. Thus, in case of large temperatures the cosmological constant takes on a negative value in the limit 𝑘 → 0 which was also initially predicted by certain string theories, however, in our approach this is not in disagreement with observations, since during the thermal evolution of the Universe a phase transition occurs and the cosmological constant runs to the expected positive value at low temperatures.