With non-perturbative de Sitter gravity and holography in mind, we deduce the
genus expansion of de Sitter Jackiw-Teitelboim (dS JT) gravity. We find that
this simple model of quantum cosmology has an effective string coupling which
is pure imaginary. This imaginary coupling gives rise to alternating signs in
the genus expansion of the dS JT S-matrix, which as a result appears to be
Borel-Le Roy resummable. We explain how dS JT gravity is dual to a formal
matrix integral with, in a sense, a negative number of degrees of freedom.
Conclusions:
- We have examined the genus expansion of de Sitter Jackiw-Teitelboim (dS JT) gravity and found that it has an effective string coupling that is pure imaginary.
- The alternating signs in the genus expansion of the dS JT S-matrix suggest that it is Borel-Le Roy resummable.
- We have established a duality between dS JT gravity and a formal matrix integral with a negative number of degrees of freedom.
Future Roadmap:
1. Further Investigation of dS JT Gravity
- Researchers should continue exploring the implications and properties of dS JT gravity, taking into account the pure imaginary string coupling and Borel-Le Roy resummability.
- Investigate the connection between dS JT gravity and other theories or models in quantum cosmology to gain a deeper understanding of its significance.
2. Holography and Non-Perturbative de Sitter Gravity
- Explore the relationship between holography and non-perturbative de Sitter gravity, as mentioned in the introduction. Investigate how holographic principles can provide insights into the nature of de Sitter space.
- Consider the potential applications of holography in understanding the behavior of dS JT gravity and its dualities.
3. Formal Matrix Integrals
- Investigate the concept of a formal matrix integral with a negative number of degrees of freedom, which arises in the duality with dS JT gravity.
- Explore the implications and potential uses of such formal matrix integrals in other areas of theoretical physics.
4. Challenges and Opportunities
- Challenges:
- Opportunities:
Researchers may face difficulties in mathematically formulating and solving problems related to non-perturbative de Sitter gravity, holography, and formal matrix integrals.
The complex nature of the effective string coupling and the negative number of degrees of freedom in the dS JT gravity duality may require innovative approaches to analyze and understand.
Exploring the duality between dS JT gravity and formal matrix integrals could provide new perspectives on quantum cosmology and potentially lead to breakthroughs in understanding the nature of de Sitter space.
Holography can offer valuable insights and techniques for studying non-perturbative de Sitter gravity, potentially paving the way for new discoveries and connections between different areas of theoretical physics.