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, that 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 necessary for the Hamiltonian to vanish and for entropy to
exist in gravitational systems.
In this article, we examine the conclusions regarding the effective action in renormalizable quantum theory of gravity and its relationship to entropy. We also explore the concept of conformal dominance at high energy beyond the Planck scale in the context of renormalizable quantum gravity. Finally, we discuss the role of ghost modes in gravitational systems and their connection to the existence of entropy.
Conclusion 1: Conservation of Entropy in Standard Cosmology
The total Hamiltonian in renormalizable quantum theory of gravity vanishes, leading to the emergence of entropy. This conservation of entropy is a fundamental assumption in standard cosmology. By showing that the total Hamiltonian is a renormalization group invariant that remains constant throughout cosmic evolution, we can establish the conservation of entropy as an ansatz.
Conclusion 2: Quantum Gravity Inflation and the Current Entropy of the Universe
By calculating the effective action under the scenario of quantum gravity inflation, we can derive the current entropy of the universe. Quantum gravity inflation refers to the inflationary period caused by the dynamics of renormalizable quantum gravity. This calculation allows us to understand the contribution of quantum gravity to the overall entropy of the universe.
Conclusion 3: Unphysical Ghost Modes and the Vanishing Hamiltonian
We argue that ghost modes in renormalizable quantum gravity are unphysical but necessary for the Hamiltonian to vanish. Ghost modes are peculiar states that exist within gravitational systems and play a crucial role in allowing for the existence of entropy. Understanding the nature of ghost modes is essential for comprehending the relationship between gravity, entropy, and quantum effects.
Future Roadmap: Challenges and Opportunities
As we move forward in our understanding of renormalizable quantum gravity and its implications for entropy, several challenges and opportunities lie ahead:
- Development of More Precise Calculations: Further research is needed to improve the accuracy of calculating the effective action and determining the contribution of quantum gravity to the current entropy of the universe. This will require advancements in theoretical models and computational techniques.
- Investigation of Consequences of Conformal Dominance: The concept of conformal dominance at high energy beyond the Planck scale introduces intriguing possibilities for understanding the behavior of gravity and entropy. Exploring the consequences and implications of conformal dominance will open new avenues for future research.
- Resolution of the Nature of Ghost Modes: Understanding the nature of ghost modes in gravitational systems remains a challenge. Further investigations and theoretical breakthroughs are necessary to clarify their role in the vanishing Hamiltonian and the existence of entropy.
- Experimental Verification: While much of the discussion is theoretical, experimental verification is crucial to validate the conclusions and predictions made in this field. The development of experimental techniques and observational data that can test the concepts presented here will be an important focus in the future.
By addressing these challenges and capitalizing on the opportunities presented by these conclusions, we can pave the way for a deeper understanding of renormalizable quantum gravity, its connection to entropy, and its implications for our understanding of the universe.