Quantum Gravity Effective Action Provides Entropy of the Universe

The effective action in the 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.