Thermal RG flow of AS quantum gravity

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 ≡ k T = τ k (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, k T 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.