  Using spectral regularisation, we compute the Weyl anomaly and express the
anomaly generating functional of the quantum effective action through a
collective scalar degree of freedom of all quantum vacuum fluctuations. Such a
formulation allows us to describe induced gravity on an equal footing with the
anomaly-induced effective action, in a self-consistent way. We then show that
requiring stability of the cosmological constant under loop quantum
corrections, Sakharov's induced gravity and Starobinsky's anomaly-induced
inflation are either both present or both absent, depending on the particle
content of the theory.
