Interpolation formulas for asymptotically safe cosmology

Simple interpolation formulas are proposed for the description of the renormalization group (RG) scale dependences of the gravitational couplings in the framework of the 2-parameters Einstein-Hilbert (EH) theory of gravity and applied to a simple, analytically solvable, spatially homogeneous and isotropic, spatially flat model universe. The analytical solution is found in two schemes incorporating different methods of the determination of the conversion rule $k(t)$ of the RG scale $k$ to the cosmological time $t$. In the case of the discussed model these schemes turn out to yield identical cosmological evolution. Explicit analytical formulas are found for the conversion rule $k(t)$ as well as for the characteristic time scales $t_G$ and $t_\Lambda>t_G$ corresponding to the dynamical energy scales $k_G$ and $k_\Lambda$, respectively, arising form the RG analysis of the EH theory. It is shown that there exists a model-dependent time scale $t_d$ ($t_G\le t_d<t_\Lambda$) at which the accelerating expansion changes to the decelerating one. It is shown that the evolution runs from a well-identified cosmological fixed point to another one. As a by-product we show that the entropy of the system decreases monotonically in the interval $0<t\le t_\Lambda$ due to the quantum effects.