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Title: The local quantum vacuum as the Past Hypothesis Abstract: The `Past Hypothesis’, as advocated by David Albert and Barry Loewer, is the hypothesis that the world came into being in whatever particular low-entropy highly-condensed big-bang sort of macrocondition it is that the normal inferential procedures of cosmology will eventually present to us. I consider some hypotheseses about that that macrocondition is likely to be given what cosmology has already presented to us, and explore the consequences of these hypotheses for the broader (`Mentaculus’) project of grounding physics and the special sciences in the Past Hypothesis. My main conclusion is that current cosmology suggests a unique, pure quantum state (the local quantum vacuum, or `Bunch-Davies vacuum’) for the initial state of the Universe, in which case statistical-mechanical probabilities emerge from quantum probabilities without any need for an intervening statistical postulate.