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de Sitter Quantum Cosmology: Part 1
Explore the frontiers of de Sitter quantum cosmology, uncovering the mathematical structure of the universe's past, future, and deepest paradoxes.
Investigates the foundations of de Sitter quantum gravity and quantum cosmology, examining the geometry of de Sitter space, the asymptotic Gaussian normal form of metrics, and the conceptual differences between AdS, Minkowski, and de Sitter holography. It then introduces cosmological path integrals, the dS/CFT correspondence, Euclidean static patch thermodynamics, and the Hartle-Hawking no-boundary wave function.
Lecture Guide
- 1De Sitter space describes an exponentially expanding spacetime with a positive cosmological constant, characterizing both our early inflationary epoch and our far future.
- 2Asymptotically de Sitter metrics can be placed in Gaussian normal form near future conformal infinity, where the leading metric is defined up to spatial diffeomorphisms and Weyl rescalings.
- 3Quantum cosmology utilizes path integrals over bulk geometries and boundary spatial metrics to compute wave-functionals of the universe and cosmological correlators.
- 4The de Sitter static patch metric Wick rotates into a round sphere, leading to the Gibbons-Hawking entropy formula proportional to the horizon area.
Proofs, Examples & Demos
Assumed Background