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The proposed research project will explore quantum nonequilibrium in the early universe, with a view to using cosmological data to set limits on nonequilibrium violations of quantum theory at very early times. The project has three components. (1) In inflationary cosmology, the primordial perturbations originate from quantum fluctuations, so current CMB data is sensitive to the magnitude and form of early quantum nonequilibrium. (2) I have derived a general `freezing inequality' which shows that, depending on the details of the expansion, relaxation for a scalar field can be suppressed for large-wavelength modes. I will use this result to try to make definite predictions (for example for a breaking of scale invariance in the CMB above a certain length scale). (3) The suppression of relaxation for large-wavelength field modes suggests predictions for the presence of nonequilibrium in very low energy relic particles (such as gravitinos). In addition to the research described above, another component of the proposal will be to engage philosophers of physics with the results of the research. This will be done through a series of summer seminars to be delivered to the philosophy of physics group at Oxford University (principal contact there: Prof. Simon Saunders). In summer 2012 I will give a 6 lecture course on the foundations of cosmology, and in summer 2013 a further 6 lectures will be given focussing on cosmology as a probe of the foundations of quantum theory. (A course outline is given in the Project Narrative.) I will also write a review article addressed to philosophers of physics, entitled "Inflationary Cosmology and Quantum Foundations: a Guide for Philosophers".