The cosmological constant problem (CCP) and the formulation
of consistent quantum gravity belong to the shortlist of the
most important unsolved fundamental problems of physics. In
the case of CCP the problem is to explain the extremely precise
(55 orders in the Standard Model) fine-tuning between the
independent vacuum part and the induced one, that is a function
of symmetry breaking in the models of particle physics. The
situation with CCP is so difficult that it makes sense to give
up from attempting its solution and accept the need for a fine
tuning between the vacuum and induced counterparts of the
observed energy density of the vacuum. In this case, we meet
the challenging situation with the renormalization group running
of the vacuum or induced summands of the cosmological constant
at low energies.
Assuming the effective approach to quantum gravity and the
Vilkovisky-DeWitt scheme of unique effective action, one can
derive the exact, well-defined, renormalization group running
of the vacuum cosmological constant. It turns out that, owing
to the mentioned fine-tuning with the induced part, this
running imposes severe restrictions on the possible extensions
of the Minimal Standard Model of particle physics, concerning
the magnitude of the vacuum expectation value of the corresponding
Higgs fields.