Scaling behavior of the cosmological constant: Interface between quantum field theory and cosmology

In quantum field theory, the vacuum action is subject to renormalization and to the renormalization group running. Consequently, the ``cosmological constant'' is not a constant, still less should be zero. In this paper we continue with previous work, and derive the contributions of the light particles to the running of the cosmological and gravitational constants in the Standard Model, from the cosmic scale up to the Fermi scale. At higher energies the calculation is performed in a sharp cut off approximation. It is argued that the scaling dependences of the cosmological and gravitational constants do not spoil primordial nucleosynthesis. Finally, the cosmological and field-theoretical implications of the running of the cosmological constant are discussed