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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
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.
