Renormalization-group running of the cosmological constant and the fate   of the universe
  For a generic quantum field theory we study the role played by the renormalization-group (RG) running of the cosmological constant (CC) in determining the ultimate fate of the universe. We consider the running of the CC of generic origin (the vacuum energy of quantum fields and the potential energy of classical fields), with the RG scale proportional to the (total energy density$\rm{)^{1/4}}$ as the most obvious identification. Starting from the present-era values for cosmological parameters we demonstrate how the running can easily provide a negative cosmological constant, thereby changing the fate of the universe, at the same time rendering compatibility with critical string theory. We also briefly discuss the recent past in our scenario. 
B. Guberina, R. Horvat, H. Stefancic