  We consider renormalization group flow applied to the cosmological dynamical
equations. A consistency condition arising from energy-momentum conservation
links the flow parameters to the cosmological evolution, restricting possible
behaviors. Three classes of cosmological fixed points for dark energy plus a
barotropic fluid are found: a dark energy dominated universe, which can be
either accelerating or decelerating depending on the RG flow parameters, a
barotropic dominated universe where dark energy fades away, and solutions where
the gravitational and potential couplings cease to flow. If the IR fixed point
coincides with the asymptotically safe UV fixed point then the dark energy
pressure vanishes in the first class, while (only) in the de Sitter limit of
the third class the RG cutoff scale becomes the Hubble scale.
