Quantum Mechanics of the Hartle-Hawking State

The no-boundary state in de Sitter offers a compelling framework for specifying the initial conditions of our universe. Many (but famously not all) features of the state agree beautifully with empirical observations and have served as a foundation for initial conditions in inflationary cosmology. We explore its relation to entropy puzzles in de Sitter spacetimes. We then compute the norm of the no-boundary state and show that the contributions from geometries with spherical spatial slices, including the Hartle–Hawking geometry and fluctuations around it, vanish at one loop. We present preliminary evidence that these contributions also vanish at higher loops and discuss the resulting implications for theoretical cosmology.