  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. The Lorentzian path integral for quantum cosmology with a positive
cosmological constant is meaningful in this approach, but the Euclidean version
is not. Framed in this way, the resulting framework and predictions are unique.
Unfortunately, the outcome is that primordial tensor (gravitational wave)
fluctuations are unsuppressed. We prove a general theorem to this effect, in a
wide class of theories.
