Cosmological constant, renormalization group and Planck scale physics

Starting from generic quantum effects at the Planck scale M_P, we find that the renormalization group running of the cosmological constant (CC) at low energies is possible if there is a smooth decoupling of all massive particles from M_P to the mass of the lightest neutrino. We discuss the theoretical implications of this running for the old'' and new’’ cosmological constant problems. Interestingly enough, the CC running implies a strong relationship between quantum field theory and cosmology, which should be observable in the near future in experiments such as SNAP through the measurement of a cubic redshift dependence of the CC.