Two Wave Functions and dS/CFT on S^1 x S^2

Understand

We evaluate the tunneling and Hartle-Hawking wave functions on S^1 x S^2 boundaries in Einstein gravity with a positive cosmological constant.

• In the large overall volume limit the classical predictions of both wave functions include an ensemble of Schwarzschild-de Sitter black holes.
• We show that the Hartle-Hawking tree level measure on the classical ensemble converges in the small S^1 limit.
• A divergence in this regime can be identified in the tunneling state.