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Isometric Evolution in de Sitter Quantum Gravity
Jordan Cotler1, Kristan Jensen2
1Society of Fellows, Harvard University, Cambridge, Massachusetts 02138, USA.
Time evolution in de Sitter quantum gravity is isometric, not unitary. States evolving to a crunch are projected out, limiting bulk physics knowledge for deducing the de Sitter S matrix.
Area of Science:
- Quantum gravity
- Cosmology
- Theoretical physics
Background:
- De Sitter spacetime is a key model in cosmology.
- Understanding quantum gravity is crucial for describing early universe and black holes.
- Jackiw-Teitelboim gravity offers a simplified framework for quantum gravity studies.
Purpose of the Study:
- Investigate time evolution in Jackiw-Teitelboim gravity with a positive cosmological constant.
- Determine if time evolution is unitary or isometric.
- Analyze the implications for the de Sitter S matrix.
Main Methods:
- Studied a simplified model of de Sitter quantum gravity (Jackiw-Teitelboim gravity).
- Analyzed the mathematical properties of time evolution in this model.
- Identified states projected out during time evolution.
Main Results:
- Time evolution was found to be isometric, not unitary.
- States corresponding to crunching initial conditions are projected out.
- Bulk physics knowledge, even over long timescales, is insufficient to determine the de Sitter S matrix.
Conclusions:
- The isometric nature of time evolution has significant implications for quantum gravity.
- The projection of crunching states suggests a loss of information or a specific boundary condition.
- The de Sitter S matrix cannot be fully deduced from bulk physics alone in this model.
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