Interpolation Formulas for Asymptotically Safe Cosmology

Abstract

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 tG and tΛ>tG corresponding to the dynamical energy scales kG and kΛ, respectively, arising form the RG analysis of the EH theory. It is shown that there exists a model-dependent time scale td (tG≤tdtΛ) 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 0t≤tΛ due to the quantum effects.

Keywords

• renormalization group