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Abstract

We identify a fundamental obstruction to any theory of the beginning of the universe as a semi-classical quantum process, describable using complex, smooth solutions of the classical Einstein equations. The no boundary and tunneling proposals are examples of such theories. We argue that the Lorentzian path integral for quantum cosmology is meaningful and, with the use of Picard-Lefschetz theory, provides a consistent definition of the semi-classical expansion. Framed in this way, the no boundary and tunneling proposals become identified, and the resulting framework is unique. Unfortunately, the Picard-Lefschetz approach shows that the primordial fluctuations are out of control: larger fluctuations receive a higher quantum mechanical weighting. We prove a general theorem to this effect, in a wide class of theories. A semi-classical description of the beginning of the universe as a regular tunneling event thus appears to be untenable.