Quantum cosmological instabilities - with and without boundaries

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The big bang singularity might be avoided by replacing it with a theory of initial conditions, or by considering a bounce from an earlier contracting phase. I will describe how both proposals can run into difficulties with instabilities when the spacetime must be treated semi-classically (i.e. when bounces occur due to a quantum tunneling transition rather than as classically non-singular solutions). The absence of such instabilities places new restrictions on the available theories, implying a selection criterion whose consequences remain to be explored.