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(?) > t(G) corresponding to the dynamical energy scales kG and k?, 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 )=t(d) < t(?)) 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 = t(?) due to the quantum effects.