  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.
