No smooth beginning for spacetime

Understand

We identify a fundamental obstruction to any theory of the beginning of the universe, formulated as a semiclassical path integral.

• Hartle and Hawking's no boundary proposal and Vilenkin's tunneling proposal are examples of such theories.
• Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries.
• We introduce a new mathematical tool - Picard-Lefschetz theory - for defining the semiclassical path integral for gravity.