Scaling Laws for the Cosmological Constant

We study the expansion of the universe at late times in the case that the cosmological constant obeys certain scaling laws motivated by renormalisation group running in quantum theories. The renormalisation scale is identified with the Hubble scale and the inverse radii of the event and particle horizon, respectively. We find de Sitter solutions, power-law expansion and super-exponential expansion in addition to future singularities of the Big Rip and Big Crunch type.