  The effective action in renormalizable quantum theory of gravity provides
entropy because the total Hamiltonian vanishes. Since it is a renormalization
group invariant that is constant in the process of cosmic evolution, we can
show conservation of entropy, which is an ansatz in the standard cosmology.
Here, we study renormalizable quantum gravity that exhibits conformal dominance
at high energy beyond the Planck scale. The current entropy of the universe is
derived by calculating the effective action under the scenario of quantum
gravity inflation caused by its dynamics. We then argue that ghost modes must
be unphysical but are necessary for the Hamiltonian to vanish and for entropy
to exist in gravitational systems.
